algebra question

Question

A state’s population as a function of time t (in years) is given by P(t) = 34,178,000 + 78,000t and its health care costs are given by C(t) = 47,863,000 + 430,500t + 178t2 a. Create the function representing the state’s per capita health care costs (i.e., the average cost per citizen). b. Find the average rate of change in the per capita health care cost from year 7 to year 12.

Answer 1

Hello, thank you for taking the time to post your question!

The state’s per capita health care costs can be found by dividing the total costs function by the population function.

It will be a messy expression when you plug in all the exact values but essentially you would be taking

F(t) = C(t) / P(t) in order to find the per capital health care.

For average rate of change then you would be using the general form

[F(12) – F(7)] / (12 – 7)

When I plug in the values I end up getting 0.0091 for the end value of that calculation

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions about the process to solve beyond that :)