Let \(f\) be the function defined by \(f(x)=2+2 \sqrt{5-x}\). Find $f(-4), f(1), f\left(\frac{11}{4}\right)\(, and \)f(x+5)$.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. Suppose \(C(x)=c x+F\) and \(R(x)=s x\) are the cost and revenue functions of a certain firm. Then, the firm is operating at a break-even level of production if its level of production is \(F /(s-c)\).

SoLAR PowER More and more businesses and homeowners are installing solar panels on their roofs to draw energy from the Sun's rays. According to the U.S. Department of Energy, the solar cell kilowatt-hour use in the United States (in millions) is projected to be $$ S(t)=0.73 t^{2}+15.8 t+2.7 \quad(0 \leq t \leq 8) $$ in year \(t\), with \(t=0\) corresponding to the beginning of \(2000 .\) What was the projected solar cell kilowatt-hours used in the United States at the beginning of \(2006 ?\) At the beginning of \(2008 ?\)

DruG DosaGES A method sometimes used by pediatricians to calculate the dosage of medicine for children is based on the child's surface area. If \(a\) denotes the adult dosage (in milligrams) and if \(S\) is the child's surface area (in square meters), then the child's dosage is given by $$ D(S)=\frac{S a}{1.7} $$ a. Show that \(D\) is a linear function of \(S\). Hint: Think of \(D\) as having the form \(D(S)=m S+b\). What are the slope \(m\) and the \(y\) -intercept \(b\) ? b. If the adult dose of a drug is \(500 \mathrm{mg}\), how much should a child whose surface area is \(0.4 \mathrm{~m}^{2}\) receive?

Find the points of intersection of the graphs of the functions. \(f(x)=0.2 x^{2}-1.2 x-4 ; g(x)=-0.3 x^{2}+0.7 x+8.2\)

PREVALENCE OF ALZHEIMER's PATIENTS Based on a study conducted in 1997 , the percent of the U.S. population by age afflicted with Alzheimer's disease is given by the function \(P(x)=0.0726 x^{2}+0.7902 x+4.9623 \quad(0 \leq x \leq 25)\) where \(x\) is measured in years, with \(x=0\) corresponding to age \(65 .\) What percent of the U.S. population at age 65 is expected to have Alzheimer's disease? At age 90 ?