91Ó°ÊÓ

In a laboratory culture, the number \(N(d)\) of bacteria (in thousands) at temperature \(d\) degrees Celsius is given by the function $$ N(d)=\frac{-90}{d+1}+20 \quad(4 \leq d \leq 32) $$ The temperature \(D(t)\) at time \(t\) hours is given by the function \(D(t)=2 t+4 \quad(0 \leq t \leq 14)\) (a) What does the composite function \(N \circ D\) represent? (b) How many bacteria are in the culture after 4 hours? After 10 hours?

Jack and Jill are salespersons in the suit department of a clothing store. Jack is paid \(\$ 200\) per week plus \(\$ 5\) for each suit he sells, whereas Jill is paid \(\$ 10\) for every suit she sells. (a) Let \(f(x)\) denote Jack's weekly income, and let \(g(x)\) denote Jill's weekly income from selling \(x\) suits. Find the rules of the functions \(f\) and \(g\). (b) Use algebra or a table to find \(f(20)\) and \(g(20), f(35)\) and \(g(35), f(50)\) and \(g(50)\) (c) If Jack sells 50 suits a week, how many must Jill sell to have the same income as Jack?

A rectangular region of 6000 square feet is to be fenced in on three sides with fencing costing \(\$ 3.75\) per foot and on the fourth side with fencing costing \(\$ 2.00\) per foot. Express the cost of the fence as a function of the length \(x\) of the fourth side.