Question

Suppose the population of kangaroos in a province of Australia is modeled by the following, with t=0 representing the year 2020:

P(t)=76⋅(1.84)^t
Find P(10)
a. P(10)=229.17
a. P(10)=230.08
a. P(10)=228.16
a. P(10)=239.17

Answer 1

The correct population for P(10) using the exponential growth model given as P(t)=76⋅(1.84)^t is approximately 49350.4, which is not among the provided answer choices.

Step-by-step explanation:

The student is asked to calculate P(10) using the given exponential population growth model P(t) = 76⋅(1.84)t, where P(t) is the population of kangaroos at time t years from the year 2020. To find the population at t = 10 (which is the year 2030), the formula is applied with t = 10:

P(10) = 76⋅(1.84)10

Calculating this expression using a calculator:

P(10) = 76⋅(1.84)10 ≈ 76⋅(649.6105) ≈ 49350.4

None of the provided answer choices match the correct calculation. The correct answer to the student's problem would be P(10) ≈ 49350.4, not the options given (229.17, 230.08, 228.16, or 239.17).