91Ó°ÊÓ

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. \(P=\$ 7000 ; r=6 \% ; t=5\) yr, compounded monthly

Write an equivalent exponential equation. $$ \log _{2} 8=3 $$

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. \(P=\$ 12,000 ; r=5.7 \% ; t=6\) yr, compounded quarterly

Write an equivalent exponential equation. $$ \log _{a} J=K $$

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. \(P=\$ 800 ; r=3.8 \% ; t=2 \mathrm{yr},\) compounded monthly

U.S. patents. The number of applications for patents, \(N,\) grew dramatically in recent years, with growth averaging about \(5.8 \%\) per year. That is, \(N^{\prime}(t)=0.058 N(t)\) a) Find the function that satisfies this equation Assume that \(t=0\) corresponds to \(2009,\) when approximately 483,000 patent applications were received. b) Estimate the number of patent applications in 2020 c) Estimate the doubling time for \(N(t)\).

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?

If an amount \(P_{0}\) is invested in the Mandelbrot Bond Fund and interest is compounded continuously at \(5.9 \%\) per year, the balance \(P\) grows at the rate given by \(\frac{d P}{d t}=0.059 P\) a) Find the function that satisfies the equation. Write it in terms of \(P_{0}\) and 0.059 b) Suppose \(\$ 1000\) is invested. What is the balance after I yr? After 2 yr? c) When will an investment of \(\$ 1000\) double itself?

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

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