91Ó°ÊÓ

Differentiate. $$ y=e^{8 x} $$

Solve for \(x\). $$ \log _{x} 32=5 $$

Substance \(A\) decomposes at a rate proportional to the amount of \(A\) present. a) Write an equation that gives the amount \(A\) left of an initial amount \(A_{0}\) after time \(t\). b) It is found that \(8 \mathrm{~g}\) of \(A\) will reduce to \(4 \mathrm{~g}\) in \(3 \mathrm{hr}\). After how long will there be only 1 g left?

Home mortgages. The Hogansons purchase a new home for \(\$ 195,000\). They make a \(25 \%\) down payment and finance the remainder with a 30 -yr mortgage at an annual interest rate of \(5.2 \%,\) compounded monthly. a) Find the Hogansons' monthly mortgage payment. b) Assume that the Hogansons make every payment for the life of the loan. Find their total payments. c) How much interest do the Hogansons pay over the life of the loan?

Mortgages. Andre purchases an office building for \(\$ 450,000 .\) He makes a \(30 \%\) down payment and finances the remainder through a 15-yr mortgage at an annual interest rate of \(4.15 \%,\) compounded monthly. a) Find Andre's monthly mortgage payment. b) Assume that Andre makes every payment for the life of the loan. Find his total payments. c) How much interest does Andre pay over the life of the loan?

Hardy Bank advertises that it compounds interest continuously and that it will double your money in \(12 \mathrm{yr}\). What is its annual interest rate?

The growth rate of the demand for coal in the world is \(4 \%\) per year. When will the demand be double that of \(2006 ?\)

Solve for \(x\). $$ \log _{4} 1 / 16=x $$

Differentiate. $$ y=\log _{23} x $$

Credit cards. Isaac uses his credit card to finance a \(\$ 1200\) purchase. His card charges an annual interest rate of \(19.25 \%,\) compounded monthly, and assumes a 10 -yr term. Assume that Isaac makes no further purchases on his credit card. a) Find Isaac's monthly credit card payment. b) Assume that Isaac makes every payment for the life of the loan. Find his total payments. c) How much interest does Isaac pay over the life of the loan?