Question 1

The initial value of an exponential function is 16, and the growth factor is 1.02.If t is the independent variable, for what value of t does the function have the value 46? Round your answer to two decimal places. ​

Accepted Answer

The answer of The initial value of an exponential function...

Question 2

A population is growing exponentially with a weekly growth factor of 1.03.What is the yearly growth factor? Round your answer to two decimal places. ​

Accepted Answer

The yearly growth factor can be calculated by raising the weekly growth factor to the power of the number of weeks in a year (52). So, $1.03^{52} \approx 4.65$.

Question 3

Solve the equation  .Round your answer to two decimal places. ​

Accepted Answer

The answer of Solve the equation  .Round your answer...

Question 4

Next year's value of quantity 1 is obtained by multiplying this year's value of quantity 1 by 1.13.Next year's value of quantity 2 is obtained by adding 1.13 to this year's value of quantity 1.Which of the two quantities are growing exponentially? ​

Accepted Answer

Quantity 1 grows exponentially because its value each year is obtained by multiplying the previous year's value by a constant factor (1.13). Quantity 2 grows linearly, not exponentially, because a constant value (1.13) is added to it each year.

Question 5

Solve the exponential equation  .Round your answer to two decimal places. ​

Accepted Answer

The answer of Solve the exponential equation  .Round your...

Question 6

Select the graph of  . ​
​

Accepted Answer

The answer of Select the graph of  . ​
​
...

Question 7

A population is growing exponentially with a yearly growth factor of 1.24.What is the monthly growth factor? Round your answer to two decimal places.

Accepted Answer

The monthly growth factor can be found by taking the 12th root of the yearly growth factor (1.24) because there are 12 months in a year. This calculation gives us approximately 1.02 when rounded to two decimal places.

Question 8

Next year's value of quantity 1 is obtained by multiplying this year's value of quantity 1 by 0.75.Next year's value of quantity 2 is obtained by adding 0.75 to this year's value of quantity 1.Which of the two quantities are decaying exponentially? ​

Accepted Answer

Quantity 1 is decaying exponentially because its value each year is obtained by multiplying the previous year's value by a constant factor (0.75). Quantity 2 is not decaying exponentially; it is increased by a constant amount (0.75) each year, which is a linear change, not exponential.

Question 9

The initial value of one exponential function is 40, and the growth factor is 1.05.The initial value of a second exponential function is 90, and the decay factor is 0.95.If  is the independent variable for both functions, for what value of t are the two functions equal? Round your answer to two decimal places. ​

Accepted Answer

The answer of The initial value of one exponential function...

Question 10

Over a certain time period the price of gold doubled every 4 years.What was the yearly growth factor for gold during this period? Round your answer to two decimal places. ​

Accepted Answer

The yearly growth factor can be found using the formula for compound interest: (final amount/initial amount)^(1/number of years). Since the price doubles every 4 years, the growth factor is 2^(1/4) ≈ 1.19.

Question 11

The half-life of a certain radioactive substance is 9 years.What is the yearly decay factor? Round your answer to two decimal places. ​

Accepted Answer

The yearly decay factor is calculated using the formula: decay factor = (1/2)^(1/half-life). For a half-life of 9 years, the decay factor is (1/2)^(1/9) ≈ 0.93.

Question 12

Solve the inequality  .Round your answer to two decimal places. ​

Accepted Answer

The answer of Solve the inequality  .Round your answer...

Question 13

Next year's value of a certain quantity is obtained by multiplying this year's value of the quantity by 1.71.Which of the following can you conclude? ​

Accepted Answer

The quantity grows exponentially because each year it is multiplied by a constant factor greater than 1 (1.71), indicating exponential growth.

Question 14

Solve the inequality  .Round your answer to two decimal places. ​

Accepted Answer

The answer of Solve the inequality  .Round your answer...

Question 15

A radioactive substance is decaying exponentially with yearly decay factor 0.93.What is the monthly decay factor? Round your answer to two decimal places. ​

Accepted Answer

The yearly decay factor is 0.93, which means the substance retains 93% of its amount each year. To find the monthly decay factor, we take the 12th root of 0.93 (since there are 12 months in a year), which gives approximately 0.99. This represents the substance retaining 99% of its amount each month.

Question 16

Solve the equation  .Round your answer to two decimal places. ​

Accepted Answer

The answer of Solve the equation  .Round your answer...

Question 17

For a certain substance, we get next week's amount by dividing by 5.That means the amount is showing exponential decay.What is the weekly decay factor? Round your answer to two decimal places. ​

Accepted Answer

The weekly decay factor is the multiplier used to find the amount of substance for the next period. Since the substance's amount is divided by 5 each week, the decay factor is 1/5 or 0.20 when rounded to two decimal places.

Question 18

Select the graph of  . ​
​

Accepted Answer

The answer of Select the graph of  . ​
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...

Question 19

Next year's value of a certain quantity is obtained by multiplying this year's value of the quantity by 0.74.Which of the following can you conclude? ​

Accepted Answer

The quantity decays exponentially because each year it is multiplied by a constant factor (less than 1), which is characteristic of exponential decay.

Question 20

Solve the exponential equation  .Round your answer to two decimal places. ​

Accepted Answer

The answer of Solve the exponential equation  .Round your...

Quiz 16: Exponential Growth and Decay

The initial value of an exponential function is 16, and the growth factor is 1.02.If t is the independent variable, for what value of t does the function have the value 46? Round your answer to two decimal places. ​

A population is growing exponentially with a weekly growth factor of 1.03.What is the yearly growth factor? Round your answer to two decimal places. ​

Solve the equation .Round your answer to two decimal places. ​

Next year's value of quantity 1 is obtained by multiplying this year's value of quantity 1 by 1.13.Next year's value of quantity 2 is obtained by adding 1.13 to this year's value of quantity 1.Which of the two quantities are growing exponentially? ​

Solve the exponential equation .Round your answer to two decimal places. ​

Select the graph of . ​ ​

A population is growing exponentially with a yearly growth factor of 1.24.What is the monthly growth factor? Round your answer to two decimal places.

Next year's value of quantity 1 is obtained by multiplying this year's value of quantity 1 by 0.75.Next year's value of quantity 2 is obtained by adding 0.75 to this year's value of quantity 1.Which of the two quantities are decaying exponentially? ​

Over a certain time period the price of gold doubled every 4 years.What was the yearly growth factor for gold during this period? Round your answer to two decimal places. ​

The half-life of a certain radioactive substance is 9 years.What is the yearly decay factor? Round your answer to two decimal places. ​

Solve the inequality .Round your answer to two decimal places. ​

Next year's value of a certain quantity is obtained by multiplying this year's value of the quantity by 1.71.Which of the following can you conclude? ​

Solve the inequality .Round your answer to two decimal places. ​

A radioactive substance is decaying exponentially with yearly decay factor 0.93.What is the monthly decay factor? Round your answer to two decimal places. ​

Solve the equation .Round your answer to two decimal places. ​

For a certain substance, we get next week's amount by dividing by 5.That means the amount is showing exponential decay.What is the weekly decay factor? Round your answer to two decimal places. ​

Select the graph of . ​ ​

Next year's value of a certain quantity is obtained by multiplying this year's value of the quantity by 0.74.Which of the following can you conclude? ​

Solve the exponential equation .Round your answer to two decimal places. ​

The initial value of an exponential function is 16, and the growth factor is 1.02.If t is the independent variable, for what value of t does the function have the value 46? Round your answer to two decimal places.

A population is growing exponentially with a weekly growth factor of 1.03.What is the yearly growth factor? Round your answer to two decimal places.

Solve the equation .Round your answer to two decimal places.

Next year's value of quantity 1 is obtained by multiplying this year's value of quantity 1 by 1.13.Next year's value of quantity 2 is obtained by adding 1.13 to this year's value of quantity 1.Which of the two quantities are growing exponentially?

Solve the exponential equation .Round your answer to two decimal places.

Select the graph of .

Next year's value of quantity 1 is obtained by multiplying this year's value of quantity 1 by 0.75.Next year's value of quantity 2 is obtained by adding 0.75 to this year's value of quantity 1.Which of the two quantities are decaying exponentially?

Over a certain time period the price of gold doubled every 4 years.What was the yearly growth factor for gold during this period? Round your answer to two decimal places.

The half-life of a certain radioactive substance is 9 years.What is the yearly decay factor? Round your answer to two decimal places.

Solve the inequality .Round your answer to two decimal places.

Next year's value of a certain quantity is obtained by multiplying this year's value of the quantity by 1.71.Which of the following can you conclude?

Solve the inequality .Round your answer to two decimal places.

A radioactive substance is decaying exponentially with yearly decay factor 0.93.What is the monthly decay factor? Round your answer to two decimal places.

Solve the equation .Round your answer to two decimal places.

For a certain substance, we get next week's amount by dividing by 5.That means the amount is showing exponential decay.What is the weekly decay factor? Round your answer to two decimal places.

Select the graph of .

Next year's value of a certain quantity is obtained by multiplying this year's value of the quantity by 0.74.Which of the following can you conclude?

Solve the exponential equation .Round your answer to two decimal places.