a farmer estimates that he has 9,000 bees producing honey on his farm. the farmer becomes concerned when he…

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

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

Answer

Explanation:

Step1: Determine the exponential - decay function

The general form of an exponential - decay function is $f(x)=a(1 - r)^x$, where $a$ is the initial amount, $r$ is the rate of decay as a decimal, and $x$ is the number of time - periods. Here, $a = 9000$ and $r=0.05$. So, $f(x)=9000(1 - 0.05)^x=9000(0.95)^x$. So, the first statement is false and the second statement is true.

Step2: Calculate the number of bees after 2 years

Substitute $x = 2$ into $f(x)=9000(0.95)^x$. Then $f(2)=9000\times(0.95)^2=9000\times0.9025 = 8122.5\approx8120$. So, the third statement is true.

Step3: Calculate the number of bees after 4 years

Substitute $x = 4$ into $f(x)=9000(0.95)^x$. Then $f(4)=9000\times(0.95)^4=9000\times0.81450625 = 7330.55625\neq1800$. So, the fourth statement is false.

Step4: Analyze the domain

The number of years $x$ can be any non - negative real number (for example, you could consider half - years or a fraction of a year in a more general sense), not just whole numbers. So, the fifth statement is false.

Step5: Analyze the range

The number of bees must be a non - negative whole number because you can't have a fraction of a bee in this context. So, the sixth statement is true.

Answer:

B. The function $f(x)=9000(0.95)^x$ represents the situation. C. After 2 years, the farmer can estimate that there will be about 8,120 bees remaining. F. The range values, in the context of the situation, are limited to whole numbers.