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 numbers

Answer 1

This is an exponential equation of the form:

y=ab^x, where a=initial value and b=common ratio or "rate"

In this case a=9000 and b=(100-5)/100=0.95 so

f(x)=9000(0.95)^x

After two years...

f(2)=9000(0.95)^2=8122.5....so I guess that you could estimate that there are about 8120 bees left to the nearest 10 bees.

however f(4)≈7331, far more than 1800

In reality, the domain is not really limited to whole values, unless we are to believe that the 5% die off in an instant at the end of each year :)

The range is the number of bees, and as such, you cannot have fractional bees, thus the range, in reality, is limited to whole numbers.

Answer 2

Explanation:

1. The function f(x) = 9,000(0.95)x represents the situation.

2. After 2 years, the farmer can estimate that there will be about 8,120 bees remaining.

3. The range values, in the context of the situation, are limited to whole numbers.