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

To find f(3), we can use the formula for an exponential decay function: f(t) = A x e^(kt), where A is the initial value, t is the time, and k is the decay factor. In this case, we are given that A = 300 and k = 0.091. Plugging in these values, we get f(t) = 300 x e^(0.091t). To find f(3), we substitute t = 3 into the formula and evaluate the expression to get f(3) ≈ 213.3620 (rounded to four decimal places).

Step-by-step explanation:

To find f(3), we can use the formula for an exponential decay function:

f(t) = A × e^(kt)

Where A is the initial value, t is the time, and k is the decay factor. In this case, we are given that A = 300 and k = 0.091. Plugging in these values, we get:

f(t) = 300 × e^(0.091t)

To find f(3), we substitute t = 3 into the formula:

f(3) = 300 × e^(0.091 × 3)

Using a calculator, we evaluate this expression to get f(3) ≈ 213.3620 (rounded to four decimal places).