Unit 7 Review

How do you solve log problems?

How do you solve when x is in the exponent?

How is a problem like $8^{\left(x+3\right)}=756$  different from a problem like  $8^x=756$  ?  Explain the process for solving each of these problems and their similarities and differences.

A certain type of bacteria grows in population by 14% every hour. Given that there were 100 bacteria to start with, answer the following questions.

a. Write an equation to model the situation.

b. How many bacteria will there be in a day?

c. When will there be 500 bacteria? Round to the nearest hour.

Scrooge McDuck is saving money in his bank account. In 2021, his money will have grown to $3300. If he originally deposits $1500 in the year 2015, write a function for the exponential growth of his money in the bank account.

 $f\left(0\right)=1500$  

 $f\left(6\right)=3300$  

A car was originally purchased in May 2011 for $35,000. The car depreciates at a rate of 18% every year.

a. Write a function that will represent the value of the car after n years.

b. What will the value of the car be in 2021?

c. When will the car be worth half of its original value?