Question

00a day 7 test 5 semester 1

a population of 1200 rabbits increases by 2.5% each year. at the end of 5 years, there will be approximately 1,358 rabbits in the population. which function can be used to determine the number of rabbits, (y), in this population at the end of (t) years?

a. (y = 1200(1 - 0.025)^t)
b. (y = 1200(1 + 0.025)^t)
c. (y = 1200(0.025)^t)
d. (y = 1200(2.5)^t)

Explanation:

Identify the initial value

Using the Exponential Functions knowledge point

$$ a = 1200 $$

Determine the growth rate

Using the Exponential Growth knowledge point

$$ r = 2.5\% = 0.025 $$

Formulate the exponential growth function

Using the Exponential Growth and Exponential Functions knowledge points

$$ y = a(1 + r)^t $$

$$ y = 1200(1 + 0.025)^t $$

Answer:

• A. \(y = 1200(1 - 0.025)^t\)
• B. \(y = 1200(1 + 0.025)^t\) (Correct answer)
• C. \(y = 1200(0.025)^t\)
• D. \(y = 1200(2.5)^t\)