1. Increased longevity and the aging of the baby boom generation - those
born between 1946 and 1965 - are the primary reasons for a rising median
age. The median age (in years) of the U.S. population from 1900 through
2011 is approximated by the function
$\begin{aligned} f(t) = \begin{cases} 1.3t + 22.9 & 0 \le t \le 3\\ -0.7t^2 + 7.2t + 11.5 & 3 < x \le 7\\ 2.6t + 9.4 & 7 < x \le 11 \end{cases} \end{aligned}$ where $t$ is measured in
decades, with $t = 0$ corresponding to the beginning of 1900. What was the
median age of the U.S. population at the beginning of 1980? Round your
answer to two decimal places, and use units and context.
2. The function $f(x)$ represents the total cost, in dollars, of producing $x$ units.
The function $h(t)$ represents how many units are produced at time $t$. How
could we combine these two functions to form a function that gives the
total cost as a function of time? Write an expression for that function in
terms of $f$ and $h$.
