Unit 7 Review

Unit 7 Review

March 18th and 19th

Logarithms

Remeber that the logarithm is written as  $\log_by=x$  so that means that it can be rewritten as an exponential equation  $b^{x\ }=\ y$  .

Multiple Choice

Solve for x.

 $\log_7x=4$  

• 16384

• 2401

• 11

• 1.75

Open Ended

How do you solve log problems?

Change of Base

When you have  $b^x=y$  you can solve for x by using the change of base, meaning you will take the logof the solution and divide it by the log of the base. 

 $\frac{\log_{\ }y}{\log_{ }b}$  

Multiple Choice

Solve thegiven problem

 $5^x=35$  

•  $7$  

•  $\frac{1}{7}$  

•  $1.670$  

•  $2.209$  

Open Ended

How do you solve when x is in the exponent?

Multiple Choice

Solve for x.

 $10\left(1.2\right)^x=30$  

•  $1.444$  

•  $1.369$  

•  $1.578$  

•  $6.026$  

Multiple Choice

Solve for x.

 $8\left(2\right)^{\left(x-2\right)}=256$  

• 7

• 4

• 0

Multiple Choice

Solve for x.

 $16\left(2.4\right)^{\left(x-2\right)}=200$  

• 3.452

• 4.885

• 3.595

Open Ended

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.

Open Ended

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.

Open Ended

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.

 $f\left(0\right)=1500$  

 $f\left(6\right)=3300$  

Open Ended

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?