91Ó°ÊÓ

Write an equivalent exponential equation. $$ -\log _{b} V=w $$

Differentiate. $$ y=7^{x^{4}+2} $$

Find the payment amount p needed to amortize the given loan amount. Assume that a payment is made in each of the n compounding periods per year. \(P=\$ 150,000 ; r=5.15 \% ; t=30 \mathrm{yr},\) compounded semiannually

Find the half-life for each situation. An investment loses \(1.9 \%\) of its value every week.

Write an equivalent exponential equation. $$ -\log _{10} h=p $$

Pete Zah's, Inc., is selling franchises for pizza shops throughout the country. The marketing manager estimates that the number of franchises, \(N,\) will increase at the rate of \(10 \%\) per year, that is, \(\frac{d N}{d t}=0.10 \mathrm{~N}\) a) Find the function that satisfies this equation. Assume that the number of franchises at \(t=0\) is 50 b) How many franchises will there be in 20 yr? c) In what period of time will the initial number of 50 franchises double?

Find the payment amount p needed to amortize the given loan amount. Assume that a payment is made in each of the n compounding periods per year. \(P=\$ 150,000 ; r=5.15 \% ; t=30 \mathrm{yr},\) compounded semiannually

Differentiate. $$ y=4^{x^{2}+5} $$

Iodine-131 has a decay rate of \(9.6 \%\) per day. The rate of change of an amount \(N\) of iodine- 131 is given by $$\frac{d N}{d t}=-0.096 N$$ where \(t\) is the number of days since decay began. a) Let \(N_{0}\) represent the amount of iodine- 131 present at \(t=0 .\) Find the exponential function that models the situation. b) Suppose \(500 \mathrm{~g}\) of iodine- 131 is present at \(t=0\). How much will remain after 4 days? c) After how many days will half of the \(500 \mathrm{~g}\) of iodine-13l remain?

Graph. $$ y=2.6(0.8)^{x} $$