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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 4 to year 8.

Answer 1

a. Let A(t) be Average per citizen cost, then A(t)=C(t)/P(t),

b. Average rate of change in the per capita health care cost from year 4 to year 8 will be[A(8)-A(4)]/(8-4), just plug in 8 and 4 and calculate it.

Remember that average rate of change is the slope of the secant line between any two points of the function.