Exam 13: Exponential and Logarithmic Functions

Solve the problem. -The population of a particular country was 24 million in 1980; in 1994, it was 32 million. The exponential growth function describes the population of this country t years after 1980. Use the fact that 14 years After 1980 the population increased by 8 million. Find k rounded to three decimal places.

Evaluate. -

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

Evaluate. -

Use a calculator to solve the equation. Round the answer to the nearest hundredth. -

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

A one-to-one function f is given. Find f-1(x) and graph f(x) with a solid line and f-1(x) with a dotted line on the same axes. -

Determine whether the function is a one-to-one function. -

For the given functions f and g , find the indicated composition. -

Use the definition of a logarithm to find an equivalent equation. -

Find the unknown value. -

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

Evaluate. -

Solve the problem. -A sample of 800 g of lead-210 decays to polonium-210 according to the function given by , where t is time in years. What is the amount of the sample, to the nearest gram, after 100 years?

For the given function, find the domain and range of both f(x) and f-1(x). -{(6, -11), (-1, -10), (-3, -9), (-5, -8)}

Determine whether the function is a one-to-one function. -

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function. -

Solve the equation. -

Solve the problem. -The amount of a radioactive substance present, in grams, at time t in months is given by the formula y = 8000(2)-0.2t. Find the number of grams present in 3 years. If necessary, round to three decimal places.

Write the equation in exponential form. -