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
Answer
A
The function f(x) = 9,000(1.05)x represents the situation.
B
The function f(x) = 9,000(0.95)x represents the situation.
C
After 2 years, the farmer can estimate that there will be about 8,120 bees remaining.
D
After 4 years, the farmer can estimate that there will be about 1,800 bees remaining.
E
The domain values, in the context of the situation, are limited to whole numbers.
F
The range values, in the context of the situation, are limited to whole numbers.
Explanation
A 5% yearly decrease means 95% of the population remains each year, so the model is f(x) = 9,000(0.95)^x. After 2 years, 9,000(0.95)^2 = 8,122.5, or about 8,120 bees. The number after 4 years is about 7,337, not 1,800. Years can include fractional values, but the number of bees in the population must be a whole number.
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