Question

Suppose that f is an exponential function with decay factor 0.091 and that f(0) = 300. find f(3). (round your answer to four decimal places.)

Answer 1

f(3) is found by plugging x = 3 into the exponential decay function f(x) = 300 * e^(-0.091x), calculating the value of the exponential term, and multiplying by the initial amount 300.

Step-by-step explanation:

The student's question asks to find the value of f(3) for an exponential function with a decay factor and an initial value. We are given that the decay factor is 0.091 and that f(0) = 300. An exponential decay function is generally given by f(x) = a * e(-kx), where 'a' is the initial amount, 'k' is the decay constant, and 'x' is the time.

In this case, 'a' is 300, and the decay factor 'k' is 0.091, so the function becomes f(x) = 300 * e(-0.091x). To find f(3), we simply substitute 'x' with 3:

f(3) = 300 * e(-0.091*3)

Now we need to calculate the value of e(-0.273) and multiply that by 300. After performing this calculation, we round the result to four decimal places.