In 1998, the population of country C was 38 million, and the exponential growth rate was 1% per year
Answers
Answer:
Step-by-step explanation:
Formula for the exponential graph is given by the function,
\(P(t) = P_0(1 + r)^t\)
Where \(P(t)\) = population after 't' years
\(P_0\) = Initial population
r = rate of increase
t = Number of years
In 1988, population of a country C was 30 million.
A). Function for the population will be,
\(P(t)=38(1+0.01)^t\)
\(=38(1.01)^t\)
B). Population in year 2020,
\(P(22)=38(1.01)^{22}\)
= 47.30 million
C). Doubling time means the duration in which \(P_0\) becomes \(2(P_0)\).
\(P(t)=2P_0\)
\(2P_0=P_0(1.01)^t\)
\((1.01)^t=2\)
By taking log on both the sides of the equation,
t[log(1.01)] = log2
t = \(\frac{\text{log}(2)}{\text{log}(1.01)}\)
= \(\frac{0.30103}{0.004321}\)
t = 69.66 years
Related Questions
Kala will rent a car for a day. The rental company offers two pricing options: Option A and Option B. For each
pricing option, cost (in dollars) depends on miles driven, as shown below.
no 1
Option A
Option 3
Cost
10
(in dollars)
TO
Miles driven
Х
5
?
(a) If Kala drives the rental car 300 miles, which option costs more?
Option A Option B
How much more does it cost than the other option?
so
(b) For what number of miles driven do the two options cost the same?
If Kala drives more than this amount, which option costs more?
Option A Option B
Answers
what is the percent increase from 3.5 to 3.5
Answers
Answer:
0
Step-by-step explanation:
There is no increase
Answer:
0
Step-by-step explanation:
there is no increase in percent
Jeremy needs 1/2 cup of milk for 2/3 cup of oats how many cups of milk is needed for each cup of oats
Answers
Using the principle of proportional relationship, the number of milk cups required per cup of oat is 0.75 cups
Setting up a proportional relationship between milk and oat :
1/2 cups = 2/3 cups
x cups = 1 cup
Cross multiply :
(2/3)x = 1/2
0.666666x = 0.5
Divide both sides by 0.66666 to isolate x
x = 0.5 / 0.666666
x = 0.75
Therefore, 0.75 cups of milk is required per cup of oat.
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Please help, thanks!
Answers
The change in function values is f(40) - f(10) = 49 - 55 = -6.
The change in x-values is 40 - 10 = 30.
Therefore, the average rate of change is -6/30, which simplifies to -1/5.
The average rate of change of the function over the interval 10 < x ≤ 40 is -1/5.
a valley is 94 feet below sea level. what is the absolute value of the elevation difference between the valley and the sea level?
Answers
The absolute value of the elevation difference between the valley and sea level is 94 feet.
The absolute value of a number is the distance of that number from zero on the number line. It represents the magnitude or size of a quantity without considering its direction. In the given scenario, we are dealing with the elevation difference between a valley and sea level.
The valley is described as being 94 feet below sea level. To find the absolute value of the elevation difference, we need to ignore the negative sign and consider the magnitude of the difference.
In this case, since the valley is below sea level, the elevation difference is negative. However, when we take the absolute value, we disregard the negative sign and focus solely on the numerical value of the difference.
By applying the absolute value to the elevation difference of -94 feet, we remove the negative sign and consider only the magnitude. Thus, the absolute value of -94 is simply 94.
Therefore, the absolute value of the elevation difference between the valley and sea level is 94 feet. It indicates that the valley is 94 feet away from sea level in terms of elevation, regardless of the direction (above or below sea level). The absolute value provides a measure of the magnitude of the difference while disregarding the direction or sign associated with it.
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Find the perimeter of the following shape:
Answers
Answer:
P = 13 + 13 + 10
P = 36
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
you add up all the side lengths because that’s what perimeter is. 13+13+10, equals 36!
Grace drove 28 1/2 miles . She used 1 1/4 gallons of gasoline . What is the unit rate for miles per gallon
Answers
Answer:
hi
Step-by-step explanation:
3 squared times 3 squared simplified
Answers
Answer:
3^4
Step-by-step explanation:
3^2*3^2
3*3*3*3
3^4
Karen received a $50.75 gift card for a photo center. She used it to buy prints that cost 10 cents each. The remaining balance, B (In dollars), on the card after
buying x prints is given by the following function
B(x) = 50.75 -0.10x
What is the remaining balance on the card if Karen bought 30 prints?
Answers
Answer: 47.75
Step-by-step explanation: It explains at the end that she bought 30 prints. You would take 30 and just plug it in for X. So the formula would look like this, B(x)=50.75-0.10(30).
Determine the degree of the following sequence: 5, 12, 21, 32, 45, 60, ...1 st degree3 rd degreeo 4 th degree2 nddegree
Answers
5 12 21 32 45 60
7 9 11 13 15
First degree is the solution
PLEASE ANSWER THIS ILL GIVE BRAINLIEST
Answers
Answer:
sorry
Step-by-step explanation:
I need help ._. Can u plz help me?
Answers
Answer:
#3
Step-by-step explanation:
Your taxable wages for Social Security purposes are $1100. How much is your Social Security tax if you have previous taxable wages of $102,000?
Answers
If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.
To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.
Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.
First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:
Social Security tax = $102,000 x 0.062 = $6,324
Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:
Social Security tax = $1,100 x 0.062 = $68.20
Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.
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hich linear function has the steepest slope?
y = negative 8 x + 5
y minus 9 = negative 2 (x + 1)
y = 7 x minus 3
y + 2 = 6 (x + 10)
Answers
The function with the steepest slope is \(y = 7x - 3\).
The correct answer is C.
The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.
Let's compare the coefficients of x in each of the given functions:
\(y = -8x + 5\)
Slope: -8
\(y - 9 = -2(x + 1)\)
Simplifying, we get \(y - 9 = -2x - 2\)
Rearranging, we have \(y = -2x + 7\)
Slope: -2
\(y = 7x - 3\)
Slope: 7
\(y + 2 = 6(x + 10)\)
Simplifying, we get \(y + 2 = 6x + 60\)
Rearranging, we have \(y = 6x + 58\)
Slope: 6
Therefore, the steepest slope is the \(y = 7x - 3\).
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−39 = −0.6k
what does k equal
Answers
Answer: k=65
Step-by-step explanation:
Answer:
k=65
Step-by-step explanation:
You would need to divide -0.6 on both sides to isolate k
-39 = -0.6k Original equation
-39÷ -0.6 = -0.6k÷-0.6 Isolating the variable
-39÷-0.6 = k SImplification
65 = k The answer!!!
When multiplying or dividing 2 negative numbers, remember that the result will be positive
I hope this helps!!!
According to the U.S. Bureau of Labor Statistics (BLS), 10.7% of workers belonged to unions in 2017. By 2018,
union membership had fallen by 0.2 percentage points. Calculate the percentage change in union membership
between 2017 and 2018. Show your work. Round your result to one decimal place.
Answers
Using it's concept, the percentage change in union membership between 2017 and 2018 was of -1.9%.
How to find the percent change of an amount?The percent change of an amount is given by the change divided by the initial amount.
For this problem, the parameters are given as follows:
Change: -0.2%.Initial amount: 10.7%.Hence the percentage change is given by:
-0.2/10.7 = -0.019 = -1.9%.
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PLEASE HELP ASAP! WILL GIVE BRAINLIEST!
Answers
Answer: g it is 2x+21 ansd h is 3x+24
Step-by-step explanation:
The gardening store sells clay flower pots, which hold 8 liters of dirt, and ceramic flower pots, which hold 5 liters. Trevor bought 4 flower pots, which will hold a total of 26 liters of dirt. How many of each type of flower pot did he buy?
Answers
Explanation:
2 clay = 16 liters
2 ceramic = 10 liters
16 + 10 = 26
John paid $50 for renting a cycle for 5 hours. Which graph shows the relationship between the cost of renting a cycle for different hours? (1 point)
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1,10 and 2,20 and 3,30.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1, 50 and 2,50 and 3,50.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1, 5 and 2,10 and 3,15.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1,20 and 2,40 and 3,60.
Answers
Answer:
Graph A <==
Step-by-step explanation:
$ 50 for 5 hours......50/5 = 10...thats $ 10 per hr
so the equation would be : y = 10x...with x being the number of hrs and y being the total cost.
So ur x axis will be the hours and your y axis will be the total cost.
so ur answer is :the title of the graph is cycle renting. the x axis (the horizontal axis)...since it is the hours, will be labeled 0,1,2,3,4,5,6
the y axis (the vertical axis)...since it is the total cost, will be labeled
0,10,20,30,40,50,60. points are plotted on (1,10),(2,20), and (3,30)
Emma needs to order liquid fertilizer for her landscaping company. She plans to keep the fertilizer in a large cylindrical storage tank, but isn’t sure how much it will hold. The tank is 10 feet tall and the circular base has a radius of 5 feet. What is the volume of her storage tank?
Answers
785.4 cubic feet
Step-by-step explanation:Step 1: Start by calculating the area of the base of the storage tank. The area of a circle is calculated by: A = π*r², where r is the radius of the circle.
Step 2: For Emma’s cylindrical storage tank, the radius of the base is 5 feet. Substitute this value in the formula and calculate the area of the base, which is equal to: A = π*5² = 78.54 square feet.
Step 3: Now we need to calculate the volume of the cylindrical storage tank. The volume of a cylinder is calculated by: V = π*r²*h, where r is the radius of the circle and h is the height of the cylinder. For Emma’s tank, the height is 10 feet. Substitute these values in the formula and calculate the volume, which is equal to: V = π*5²*10 = 785.4 cubic feet.
Step 4: Therefore, Emma’s cylindrical storage tank has a capacity of 785.4 cubic feet.
If you have any additional questions or need further assistance, please let me know.
Add the first 79 terms of this sequence:
-8,-1, 6, 13, 20, ...
Answers
Answer:
Sum is 20,935.
Step-by-step explanation:
This is an arithmetic progression.
Sum:
\(S = \frac{n}{2} (2a + (n - 1)d) \)
n is the number of terms, n = 79
S is the sum
a is the first term, a = -8
d is common difference, d = -1-(-8) = 7
substitute:
\(S = \frac{79}{2} (2 \times - 8 + (79 - 1) \times 7)) \\ \\ S = \frac{79}{2} ( - 16 + 546) \\ \\ S = \frac{79}{2} (530) \\ S = 20935\)
Joe Harris has scored 102 points
on 3-pointers so far this season. He's trying to
improve on his best season when hescored 303
points on 3-point baskets. Write an inequality to
help find how many 3-point baskets he would
need to make in order to break his record.
Answers
Answer:
Just give me the 5
Step-by-step explanation:
A coordinate plane from negative 8 to 8 along the x-axis and from negative 7 to 7 along the y-axis.
Which steps should be used to graph the equation below?
y – 4 = y minus 4 equals StartFraction one-third EndFraction left-parenthesis x plus 2 right-parenthesis.(x + 2)
1. Plot the point (2, 4).
2. From that point, count left 3 units and down 1 unit and plot a second point.
3. Draw a line through the two points.
1. Plot the point (2, 4).
2. From that point, count left 1 unit and down 3 units and plot a second point.
3. Draw a line through the two points.
1. Plot the point (–2,4).
2. From that point, count left 3 units and down 1 unit and plot a second point.
3. Draw a line through the two points.
1. Plot the point (–2,4).
2. From that point, count left 1 unit and down 3 units and plot a second point.
3. Draw a line through the two points.
Answers
The steps that should be used to graph the equation include:
1. Plot the point (–2,4).
2. From that point, count left 3 units and down 1 unit and plot a second point.
3. Draw a line through the two points.
How to illustrate the information?From the information given, the equation given is:
y = 4 - 1/3(x + 2)
where,
the point is (-2, 4) and the slope is given as m = 1/3.
It should be noted that the slope is the change in y over the change in x. Therefore, the correct option that depicts this is C.
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Answer: C
Step-by-step explanation:
y - 4.6 = 12
Pls help
Answers
Answer:
y = 16.6
Step-by-step explanation:
y - 4.6 = 12
Add 4.6 to each side
y - 4.6+4.6 = 12+4.6
y = 16.6
HELP PLEASEEEEEEEEEEEEEE
Answers
Two students in your class, Hunter and Maggie, are disputing a function. Hunter says that for the function, between x = −2 and x = 2, the average rate of change is 0. Maggie says that for the function, between x = −2 and x = 2, the graph goes up through a turning point, and then back down. Explain how Hunter and Maggie can both be correct, using complete sentences. (10 points)
Answers
Answer:
Hunter and Maggie can both be correct because when the average rate of change is zero, the sum of all possible positive slopes and negative slopes on the interval will be zero. The sum of the possible positive slopes cancels out the sum of the possible negative slopes.
In this case the graph would be a parabola with the equation ax^2+bx+c where a is negative
According to hunter
In the interval [-2,2]
The average rate of change is 0According to Maggie
The graph goes up through a turning point and back downThey can be correct
Because
If sum of all positive and negative slopes is zero then average rate of change is zeRos
So there is only one possibility
It's a parabolaThe turning point is vertexThen they both are correct
What is the volume of a rectangle prism 8 inches long, 5 inches wide, and 2 inches high
Answers
Answer:
80
Step-by-step explanation:
multiply 8x 5 and 2 then you get your answer
Answer: 80 in.
Step-by-step explanation: 8 x 5 x 2 = L x W x H = 80
8x5 = 40 x 2 = 80, Sorry if im wrong
1. An acrobat is on a platform that is 25 feet in the air. She jumps down
at an initial vertical velocity of 4 ft/s. Write a quadratic function to
represent the height h of the acrobat t seconds after the jump.
If a safety net is placed 5 feet above the ground, how long will it take
for her to land safely on the net?
Answers
It will take the acrobat 1/4 of a second to land safely on the net.
What is velocity?Velocity is a physical quantity that measures the rate at which an object moves in a particular direction. It is measured in terms of distance traveled per unit of time, usually expressed in terms of meters per second (m/s). Velocity is a vector quantity, meaning it has both a magnitude and a direction. It is an important concept in physics and is used to understand the motion of objects and forces.
The quadratic equation representing the height h of the acrobat t seconds after the jump can be written as follows: \(h=-16t^2+4t+25\).
To find the time it takes for the acrobat to land safely on the net, we need to solve for t when h=5. We can do this by substituting 5 for h into the equation and solving for t:
\(h=-16t^2+4t+25\\\\5=-16t^2+4t+25\\\\=-16t^2+4t-20=0\\\\(4+\sqrt{64})/(-32)=t\\ \\t=(4+8)/(-32)\\\\t=1/4\)
Therefore, it will take the acrobat 1/4 of a second to land safely on the net.
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What are equivalent ratios for 6:2 and 18:6 and 72:24
Answers
Observing the problem, we find the smallest ratio is still not the most simplified, so
6:2 divided by two on both sides is
3:1(-1,1,5)
9
8
7-
6
5
4
3₂
-3-2-1₁
(1,5)
(0,3)
Which exponential function is represented by the graph?
Of(x)=2(3¹)
Of(x)=3(3)
Of(x)=3(2)
O f(x) = 2(2¹)
Answers
The value of the equation that defines the function is f(x) = 3(5/3)ˣ
Finding an equation defining the functionFrom the question, we have the following parameters that can be used in our computation:
(0, 3) and (1, 5)
An exponential function is represented s
y = abˣ
Where,
a = y when x = 0
So, we have
y = 3bˣ
Using the other point, we have
3b = 5
This gives
b = 5/3
So, we have
f(x) = 3(5/3)ˣ
Hence, the equation defining f is f(x) = 3(5/3)ˣ
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