Question

Many biological populations can be modeled by f(t)=f(0) e cost, where f(0) is the size of the population when t = 0. Suppose that f(0) = 1100 and c=5. Find the maximum and minimum values of f(t) and the values oft where they occur Find the maximum value(s) of f(t) and the value(s) oft where they occur.

Answer 1

The biological population modeled by f(t) = 1100e5t has no maximum value because it increases continuously over time. The minimum value is at t = 0, which is 1100, representing the initial population size.

Step-by-step explanation:

The biological population in question can be modeled by the function f(t) = f(0) ect, where f(0) = 1100 and c = 5. To find the maximum and minimum values of f(t), we need to analyze the behavior of the exponential function. Since the base of the exponential function (e) is a positive constant and c is positive, the function will increase continuously without bound, so there is no maximum value; the function will grow indefinitely as time increases. However, the minimum value of f(t) is at t = 0, which is the starting size of the population f(0) = 1100. This initial value is the minimum because as t increases, the value of ect will also increase, causing f(t) to increase.