Question

A farmer estimates that he has 9,000 bees producing honey on his farm. The farmer becomes concerned when he realizes the population of bees seem to be decreasing steadily at a rate of 5% per year. If the number of bees in the population after x years is represented by f(x), which statements about the situation are true? Check all that apply.

Answer 1

Statements 1, 2 and 3 are all correct

Explanation:

To determine which statements about the situation are true, let's analyze the given information:

1. The initial number of bees is 9,000.

2. The population of bees is decreasing at a rate of 5% per year.

Now, let's evaluate the statements:

Statement 1: The function f(x) represents the number of bees in the population after x years.

This statement is true. The function f(x) represents the number of bees in the population after x years.

Statement 2: The initial value of f(x) is 9,000.

This statement is true. The initial number of bees is given as 9,000, so the initial value of f(x) is indeed 9,000.

Statement 3: The rate of decrease in f(x) is 5% per year.

This statement is true. The problem states that the population of bees is decreasing at a rate of 5% per year.

Statement 4: The function f(x) can be represented as f(x) = 9,000 - 0.05x.

This statement is false. While the rate of decrease is 5% per year, it does not mean that the function f(x) can be represented as f(x) = 9,000 - 0.05x. The rate of decrease should be applied to the current population, not the initial population.

Therefore, the true statements are:

- Statement 1: The function f(x) represents the number of bees in the population after x years.

- Statement 2: The initial value of f(x) is 9,000.

- Statement 3: The rate of decrease in f(x) is 5% per year.