Exam 5: Exponential and Logarithmic Functions

Use the laws of logarithms to simplify the expression. ​

Find the derivative of the function. ​

Find the accumulated amount after 6 year(s) if $5,000 is invested at 8% compounded continuously. Round your answer to the nearest cent. ​ $__________

Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest hundredth. ​ 10% / year compounded semiannually ​ __________% ​ 3% / year compounded quarterly ​ __________%

Evaluate the expression. ​ ​

Solve the equation for . ​

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by ​ . Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .)

​Express the equation in logarithmic form. ​

Use the definition of a logarithm to prove . Hint: Let and . Then, and

Find the derivative of the function. ​

Evaluate the expression. ​ ​

Find the derivative of the function. ​

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ​ The function is continuous on . ​

Use logarithmic differentiation to find the derivative of the function. ​

​Express the equation in logarithmic form. ​ ​

Find the derivative of the function. ​ ​

Find the derivative of the function. ​ ​

Use the facts that and to find the value of the logarithm. ​ ​

Find the derivative of the function. ​ ​

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. ​ P = $150,000, r = 7%, t = 3, compounded daily ​