Exam 4: Exponential and Logarithmic Functions

For simple interest accounts, the amount A accumulated or due depends on the principal p, interest rate r, and the time t in years according to the formula A = p(1 + rt). Mary borrowed $7700 at 17.5% simple interest. If she repaid $18,749.50, what was the term of the loan?

Use the following to answer questions : Use a calculator (as needed) to evaluate the function as indicated. Round values to the thousandths place if necessary. P(t) = 1700 -t = 7

Use a calculator to find an approximate value, rounded to four decimal places. log 0.078

Solve the exponential equation. 100^{x - 3} = 1000^x

Use the following to answer questions : The magnitude of an earthquake is given by the equation where I is the actual intensity of the earthquake and I₀ is the reference intensity (the smallest earth movement that can be recorded on a seismograph). -Find the value of M(I) when I = 81,500I₀. Round your answer to the nearest tenth.

Solve the equation by writing it in logarithmic form. Answer in exact form.

Write the equation in the simplified form log _b x = k (logarithmic term = constant). Do not solve. 5log ₃ x + log ₃(x + 8) = -3

Use the following to answer questions : Use a calculator (as needed) to evaluate the function as indicated. Round values to the thousandths place if necessary. P(t) = 1700 -t = 8.5

If a periodic payment p is deposited n times per year, with annual interest rate r also compounded n times per year for t years, the future value of the account is given by , where . What quarterly investment amount is required to save $5300 in 7 years at an annual rate of 6% compounded quarterly? Round your answer to the nearest cent.

Prove (using compositions) that g(x) = f ^-1(x). f(x) = -3x + 1, g(x) =

Use the following to answer questions : Use a calculator (as needed) to evaluate the function as indicated. Round values to the thousandths place if necessary. P(t) = 5800 · 16^x -t =

Use the following to answer questions : A lab technician wishes to grow a culture of 800,000 bacteria, which are known to double in 16 hours. The technician begins with 9000 bacteria. -Find the growth rate r. Round your answer to the nearest hundredth.

Determine if the function is one-to-one by noting the functions family to which it belongs and mentally picturing the shape of its graph. f(x) = -|x + 7|-5

Determine the value of x by writing the equation in exponential form. log _x = -4

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph. Clearly state what shifts are applied. y = 4^-x

Graph the logarithmic function. f(x) = ln(x - 2) + 3

For accounts where interest is compounded annually, the amount A accumulated or due depends on the principal p, interest rate r, and the time t in years according to the formula A = p(1 + r)^t. What interest rate will insure a $1700 deposit will be worth $2342.24 in 5.5 years? Round your answer to the nearest tenth of a percent.

For compound interest accounts, the amount A accumulated or due depends on the principal p, interest rate r, number of compoundings per year n, and the time t in years according to the formula . Find r given A = $5462.11, p = $2950, and t = 4 years with interest compounded monthly. Round your answer to the nearest tenth of a percent.

Determine if the function is one-to-one by noting the functions family to which it belongs and mentally picturing the shape of its graph. f(x) = 8x² + 5

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph. y =