Question

1. A population of 30,000 fish is expected to shrink at a rate of 7.5% per year. Which is the best prediction for the fish population in 8 years?

Answer 1

Using the formula for exponential decay, the predicted fish population in 8 years, shrinking at a rate of 7.5% per year from an initial number of 30,000, is approximately 15,030 fish.

Step-by-step explanation:

We are to predict the fish population in 8 years assuming it shrinks at a rate of 7.5% per year from an initial population of 30,000 fish. We can use the formula for exponential decay, which is:

P(t) = P0 × (1 - r)t

where P(t) is the population at time t, P0 is the initial population, r is the decay rate (as a decimal), and t is the time in years.

Initial Population: 30,000

Annual decay rate: 7.5% or 0.075 as a decimal

Time period: 8 years

Applying these values to the formula, we get:

P(8) = 30,000 × (1 - 0.075)8

P(8) = 30,000 × (0.925)8

P(8) = 30,000 × 0.501

P(8) ≈ 15,030

So, the best prediction for the fish population in 8 years is approximately 15,030 fish.

Answer 2

P=30,000 I=PRT
R=7.5% I=30000x7.5x8
T=8yr I=18000