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 seems 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.
The function f(x) = 9,000(1.05)x represents the situation.
The function f(x) = 9,000(0.95)x represents the situation.
After 2 years, the farmer can estimate that there will be about 8,120 bees remaining.
After 4 years, the farmer can estimate that there will be about 1,800 bees remaining.
The domain values, in the context of the situation, are limited to whole numbers.
The range values, in the context of the situation, are limited to whole number

Answer 1

Answer:

• The function f(x) = 9,000(0.95)^x represents the situation.
• After 2 years, the farmer can estimate that there will be about 8,120 bees remaining.
• The range values, in the context of the situation, are limited to whole number

Step-by-step explanation:

The "growth" rate is -5%, so the growth factor, the base in the exponential equation, is 1.00-5% =0.95.

Using x=2, we find the population in 2 years is expected to be about ...

  f(2) = 9000·0.95^2 ≈ 8123 . . . . about 8120

Using x=4, we find the population in 4 years is expected to be about ...

  f(4) = 9000·0.95^4 ≈ 7331 . . . . about 7330

Since population is whole numbers of bees, the range of the function is limited to whole numbers.

The domain of the function is numbers of years. Years can be divided into fractions as small as you want, so the domain is not limited to whole numbers.

The choices listed above are applicable to the situation described.