Complete the table below.

Question

Recall that the equations for Exponential Growth is f(x) = a(1+r)t
and the Exponential Rate of Decay is f(x) = a(1−r)t

Part A: Determine if the situation is a rate of decay or growth. Write "decay" or "growth"

Part B: Determine the rate of decay or growth (r-value).

Part C: Determine the function of the scenario. Do not include commas in your equation. Simplify your function.

Scenario Decay or Growth? r-value Function

South Carolina has found that the manatee population is increasing.

In 2024, there were 1,014 manatees with a rate of increase of 3.1% per year.

growth 0.031 f(x) =
1014(1.031)t

A typical cup of tea contains about 25 milligrams (mg) of caffeine.

Every hour, approximately 3% of the amount of caffeine in the body is

metabolized and eliminated.

f(x) =

In 2024, the population of the local high school is

314 students with an annual rate of increase of 1.18%.

f(x) =

The value of a 2024 Toyota Prius was $44,205 when it went on the

market. It depreciates at a rate of 10.5% per year

f(x) =


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Answer 1

Here’s the completed table based on the scenarios provided:

| Scenario | Decay or Growth? | r-value | Function | |:------------:|:----------------:|:-------:|:------------------------------:| | South Carolina has found that the manatee population is increasing. In 2024, there were 1,014 manatees with a rate of increase of 3.1% per year. | growth | 0.031 | f(x) = 1014(1.031)^t | | A typical cup of tea contains about 25 milligrams (mg) of caffeine. Every hour, approximately 3% of the amount of caffeine in the body is metabolized and eliminated. | decay | 0.03 | f(x) = 25(0.97)^t | | In 2024, the population of the local high school is 314 students with an annual rate of increase of 1.18%. | growth | 0.0118 | f(x) = 314(1.0118)^t | | The value of a 2024 Toyota Prius was $44,205 when it went on the market. It depreciates at a rate of 10.5% per year. | decay | 0.105 | f(x) = 44205(0.895)^t |

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