Question

many biological populations can be modeled by f(t)=f(0)e^csint, where f(0) is the size of the population when t=0. Suppose that f(0)=1200 and c=5. Find the maximum and minimum values of f(t) and the values of t where they occur.

Answer 1

The population growth model f(t) = f(0)e^c sin(t) can be used to represent biological populations. To find the maximum and minimum values of f(t) and the values of t where they occur, we can use the fact that sin(t) has a maximum value of 1 and a minimum value of -1.

Step-by-step explanation:

The population growth model f(t) = f(0)e^c sin(t) can be used to represent biological populations, where f(0) is the initial population size at t=0 and c is a constant.

In this case, we are given f(0) = 1200 and c = 5.

To find the maximum and minimum values of f(t) and the values of t where they occur, we can use the fact that sin(t) has a maximum value of 1 and a minimum value of -1. Therefore:

• The maximum value of f(t) is f(0)e^c when sin(t) = 1.
• The minimum value of f(t) is f(0)e^(-c) when sin(t) = -1.