Question

A small lake is stocked with a certain species of fish. The fish population is modeled by the function

p=18/1+4e⁻⁰.⁷ᵗ

where P is the number of fish in thousands and t is measured in years since the lake was stocked.

(a) Find the fish population after 4 years. (Round your answer to the nearest whole fish.)

Answer 1

The fish population after 4 years is approximately 15,000 fish.

Step-by-step explanation:

To determine the fish population in the lake after 4 years, we will substitute t = 4 into the given population model function p=18/(1+4e⁻⁰.⁷ᵗ). Calculating this, we get p=18/(1+4e⁻⁰.⁷(4)). After computing the exponent and the division, we round to the nearest whole number as instructed.

The fish population after 4 years can be found by substituting t = 4 into the given population function p = 18/(1 + 4e^(-0.7t)).

So, p = 18 / (1 + 4e^(-0.7*4)) = 18 / (1 + 4e^(-2.8)) ≈ 14.517.

Since the population is measured in thousands, we need to round the answer to the nearest whole fish. Therefore, the fish population after 4 years is approximately 15,000 fish.