91Ó°ÊÓ

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$e^{2 x}=50$$

Use the One-to-One Property to solve the equation for \(x\). $$\left(\frac{1}{2}\right)^{x}=32$$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $$\ln x y z^{2}$$

A sport utility vehicle that costs $$\$ 23,300$$ new has a book value of $$\$ 12,500$$ after 2 years. (a) Find the linear model \(V=m t+b\). (b) Find the exponential model \(V=a e^{k t}\) (c) Use a graphing utility to graph the two models in the same viewing window. Which model depreciates faster in the first 2 years? (d) Find the book values of the vehicle after 1 year and after 3 years using each model. (e) Explain the advantages and disadvantages of using each model to a buyer and a seller.

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$500 e^{-x}=300$$

Write the logarithmic equation in exponential form. $$\ln 7=1.945 \ldots$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$1000 e^{-4 x}=75$$

Write the logarithmic equation in exponential form. $$\ln 10=2.302 \ldots$$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $$\log 4 x^{2} y$$

A laptop computer that costs $$\$ 1150$$ new has a book value of $$\$ 550$$ after 2 years. (a) Find the linear model \(V=m t+b\). (b) Find the exponential model \(V=a e^{k t}\) (c) Use a graphing utility to graph the two models in the same viewing window. Which model depreciates faster in the first 2 years? (d) Find the book values of the computer after 1 year and after 3 years using each model. (e) Explain the advantages and disadvantages of using each model to a buyer and a seller.