Exam 6: Exponential and Logarithmic Functions

Solve the problem. -The surface area of a balloon is given by where r is the radius of the balloon. If the radius isincreasing with time t, as the balloon is being blown up, according to the formula find thesurface area S as a function of the time t.

Solve the problem. -An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface of the gulf as a circle.At any time t, in minutes, after the beginning of the leak, the radius of the oil slick on the surface isr(t)= 4t ft. Find the area A of the oil slick as a function of time.

Graph the function. -

Write the word or phrase that best completes each statement or answers the question. -The price p of a certain product and the quantity sold x obey the demand equation 300. Suppose that the cost C of producing x units is Assuming that all items produced aresold, find the cost C as a function of the price p.

Graph the function. -

Find the exact value of the logarithmic expression. -

Solve the equation. -

The function f is one-to-one. Find its inverse. -

Find a formula for the inverse of the function described below. -A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C tothose in Country D is f(x)= 2(x + 20).

Graph the function. -

Evaluate the expression using the values given in the table. -

The function f is one-to-one. Find its inverse. -

Solve the problem. -The number of men dying of AIDS (in thousands)since 1987 is modeled by where xrepresents the number of years after 1987. Use this model to predict the number of AIDS deaths amongmen in 1994. Express answer rounded to the nearest hundred men.

Indicate whether the function is one-to-one. -{(6, -4), (9, -3), (7, -2), (5, -1)}

Use a calculator to evaluate the expression. Round your answer to three decimal places -

Find the domain of the composite function f ∘ g. -

Graph the function. -

Solve the problem. -The pH of a chemical solution is given by the formula where is the concentration of hydrogen ions in moles per liter.Find the pH if the

Graph the function. -

Approximate the value using a calculator. Express answer rounded to three decimal places. -