91Ó°ÊÓ

Following the birth of a child, a parent wants to make an initial investment \(P_{0}\) that will grow to \(\$ 30,000\) by the child's 20 th birthday. Interest is compounded continuously at \(6 \% .\) What should the initial investment be?

Maximum loan amount. Curtis plans to purchase a new car. He qualifies for a loan at an annual interest rate of \(7 \%,\) compounded monthly for 5 yr. He is willing to pay up to \(\$ 200\) per month. What is the largest loan he can afford?

Write an equivalent logarithmic equation. $$ M^{p}=V $$

Differentiate. $$ f(x)=\frac{1}{3} e^{-4 x} $$

Differentiate. $$ F(x)=-\frac{2}{3} e^{x^{2}} $$

Following the birth of their child, the Irwins want to make an initial investment \(P_{0}\) that will grow to \(\$ 40,000\) by the child's 20 th birthday. Interest is compounded continuously at \(5.3 \% .\) What should the initial investment be?

Maximum loan amount. The Daleys plan to purchase a new home. They qualify for a mortgage at an annual interest rate of \(4.15 \%,\) compounded monthly for \(30 \mathrm{yr}\). They are willing to pay up to \(\$ 1800\) per month. What is the largest loan they can afford?

Differentiate. $$ y=5^{x} \cdot \log _{2} x $$

Given \(\log _{b} 3=1.099\) and \(\log _{b} 5=1.609\), find each value. $$ \log _{b} \frac{1}{5} $$

Maximum loan amount. Martina plans to purchase a new home. She qualifies for a mortgage at an annual interest rate of \(4.45 \%,\) compounded monthly for 20 yr. She is willing to pay up to \(\$ 2000\) per month. What is the largest loan she can afford?