7.5 - Linear Vs. Exponential Models

7.5 - Linear Vs. Exponential Models

Step 1: Write the equation for each situation

Which option is linear and which option is exponential?

Linear:

• y=mx+b

• M = the amount being added each time

• B = the starting amount

• y = 57x + 1200

Exponential:

 $y=a\left(1\pm b\right)^x$  
a = starting amount
b = interest rate
 $y=1200\left(1+0.03\right)^x$  

Time

For both types of equations, time is the X value. For this problem, we would substitute 3 for x since it is asking how much money each account would have after 3 years.

Poll

Which option do you think would make more money?

• Option 1

• Option 2

Results:

• Option 1:

   $y=57\left(3\right)+1200$  

• $1,371.00

• Option 2:  $y=1200\left(1+0.03\right)^3$  

• $1,311.27

Multiple Choice

Which is the better option after 5 years?

• $100,000 yearly payments that increase by $25,000 each year

• $100,000 yearly payments that increase by 4.5% compounded annually

Multiple Choice

What is the best option after 10 years?

• $100,000 yearly payments that increase by $25,000

• $100,000 yearly payments that increase 4.5% compounded annually