Exam 13: Exponential and Logarithmic Functions

Solve the problem. -The function f(x) = 1 + 1.5 ln (x+1) models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball Player has practiced for two hours. After 402 days of practice, what is the average number of consecutive free Throws the basketball player makes?

Solve the problem. -The long jump record, in feet, at a particular school can be modeled by f(x) = 18.1 + 2.5 ln (x + 1) where x is the number of years since records began to be kept at the school. What is the record for the long jump 16 years after Records started being kept? Round your answer to the nearest tenth.

Evaluate. -

Solve the equation. -

For the given functions f and g , find the indicated composition. -f(x) = 8x + 5, g(x) = 2x - 1

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. -f(x) = 6x + 6

Approximate the value of x. Round to four decimal places. -

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. -

Provide an appropriate response. -The natural function is where e is the natural base.

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. -f(x) = x3 + 6

Use properties of logarithms to expand the logarithmic expression as much as possible. -

Evaluate. -

Evaluate. -

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. -f(x) = 4x

Solve the problem. -How many times more intense is an earthquake that measures 6 on the Richter scale than an earthquake that measures 3?

Approximate the value of x. Round to four decimal places. -

Graph the function. -

Use properties of logarithms to expand the logarithmic expression as much as possible. -

Determine whether the given functions are inverses of each other. -f(x) = 4x,

Solve the problem. -The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential Growth model How much did you initially invest in the account?