91Ó°ÊÓ

Show that \((f \circ g)(x)=(g \circ f)(x)=x\) \(f(x)=9 x-6 ; \quad g(x)=\frac{1}{9}(x+6)\)

A department store charges \(1.25 \%\) per month on the unpaid balance for customers with charge accounts (interest is compounded monthly). A customer charges \(\$ 200\) and does not pay her bill for 6 months. What is the bill at that time?

Use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function. $$ f(x)=3^{x-1} $$

George contemplates the purchase of 100 shares of a stock selling for $$ 15\( per share. The stock pays no dividends. The history of the stock indicates that it should grow at an annual rate of \)15 \%$ per year. How much should the 100 shares of stock be worth in 5 years?

Solve each exponential equation. Express irrational solutions in exact form. $$ 5\left(2^{3 x}\right)=8 $$

Analyzing Interest Rates on a Mortgage Colleen and Bill have just purchased a house for 650,000, with the seller holding a second mortgage of 100,000 . They promise to pay the seller 100,000 plus all accrued interest 5 years from now. The seller offers them three interest options on the second mortgage: (a) Simple interest at 6 % per annum (b) 5.5 % interest compounded monthly (c) $5.25 % interest compounded continuously Which option is best? That is, which results in paying the least interest on the loan?

Two bank accounts are opened at the same time. The first has a principal of $$ 1000$ in an account earning 5 % compounded monthly. The second has a principal of 2000 in an account earning 4 % interest compounded annually. Determine the number of years, to the nearest tenth, at which the account balances will be equal.

Use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function. $$ f(x)=1-2^{-x / 3} $$

If \(f(x)=3 x^{2}-7\) and \(g(x)=2 x+a,\) find \(a\) so that the \(y\) -intercept of \(f \circ g\) is 68 .

Surface Area of a Balloon The surface area \(S\) (in square meters) of a hot-air balloon is given by $$ S(r)=4 \pi r^{2} $$ where \(r\) is the radius of the balloon (in meters). If the radius \(r\) is increasing with time \(t\) (in seconds) according to the formula \(r(t)=\frac{2}{3} t^{3}, t \geq 0,\) find the surface area \(S\) of the balloon as a function of the time \(t\).