Exam 13: Exponential and Logarithmic Functions

Solve the problem. -Two bacteria are placed in a petri dish. The population will double every day. The formula for the number of bacteria in the dish on day t is where t is the number of days after the two bacteria are placed in the dish. How many bacteria are in the dish six Days after the two bacteria are placed in the dish?

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

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 A . By what percentage is the account increasing each year?

Find the unknown value. -

Write the equation in logarithmic form. -

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

Write the equation in logarithmic form. -9

Evaluate. -

Graph the function. -

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 given functions are inverses of each other. -

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

To what exponent must the base 10 be raised to obtain the given value? Round the answer to four decimal places. -2754

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

Write as a logarithm of a single expression. -

Write the equation in logarithmic form. -

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

Solve the problem. -The function models the amount in pounds of a particular radioactive material stored in a concrete vault, where t is the number of years since the material was put into the vault. If 400 pounds of the Material are initially put into the vault, how many pounds will be left after 190 years? Round to the nearest Pound.

Solve the problem. -The value V of a car that is t years old can be modeled by According to the model, when will the car be worth $6000? Round to the nearest tenth of a year.

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