Unit 5 Exponentials Review

Unit 5 Exponentials Review

How do we tell the difference between exponential growth and decay?

•  $y=ab^x$  

• If the "b" is greater than 1 it is growth

• If the "b" is less than 1 it is decay

Multiple Select

Choose all the equations that represent Exponential Decay.

• $y=\frac{1}{2}\cdot\left(3\right)^x$

• $y=3\cdot\left(\frac{1}{2}\right)^x$

• $y=2\cdot\left(1.01\right)^x$

• $y=5\cdot\left(.98\right)^x$

• $y=2\cdot\left(\frac{5}{2}\right)^x$

Exponential Growth

•  $f\left(x\right)=a\cdot b^x$  

• "a" represents the y-intercept of the graph and is the initial value of the function

• If you are unsure, use desmos to graph the function!
  

Exponential Growth

•  $f\left(x\right)=a\cdot b^x$  

• "b" represents the amount of growth...the bigger the number, the steeper the graph

• When in doubt, graph the function on desmos

Multiple Choice

Which function will grow the fastest?

• $f\left(x\right)=3\cdot\left(1.5\right)^x$

• $f\left(x\right)=2\cdot\left(3\right)^x$

• $f\left(x\right)=1\cdot4^x$

• $f\left(x\right)=10\cdot\left(\frac{1}{2}\right)^x$

Multiple Choice

Which function has the biggest y-intercept?

• $f\left(x\right)=\frac{1}{2}\cdot\left(10\right)^x$

• $f\left(x\right)=12\cdot\left(3\right)^x$

• $f\left(x\right)=9\cdot\left(4\right)^x$

• $f\left(x\right)=100\cdot\left(\frac{1}{2}\right)^x$

Fill in the Blanks

You set up a bank account that earns interest every year. The following function represents the amount of money in the account, t years after it is opened.

 $f\left(t\right)=200\cdot\left(1.02\right)^x$  
How much money did you initially put in the account when you first set it up?

Fill in the Blanks

You set up a bank account that earns interest every year. The following function represents the amount of money in the account, t years after it is opened.

 $f\left(t\right)=200\cdot\left(1.02\right)^x$  
What percent interest is the account increasing by each year?

Fill in the Blanks

You set up a bank account that earns interest every year. The following function represents the amount of money in the account, t years after it is opened.

 $f\left(t\right)=200\cdot\left(1.02\right)^x$  
How much is in the account after 10 years?

Linear vs Exponential

• Linear is

   $y=mx+b$  

• Exponential is  $y=a\cdot b^x$  

• Linear grows by the same amount each time, exponential grows by a different amount each time

• Exponential will eventually ALWAYS grow faster than linear

Multiple Choice

George puts $1000 in an account that adds $20 every year. Henry puts $600 in an account that increases by 5% every year. Who will have more money after 20 years?

• George

• Henry

Multiple Choice

A savings account earns 12% interest each year, compounded semi-annually (2 times a year). If you invest $200 and make no further deposits, which expression represents the balance in the account t years after it is opened?

• $200\cdot\left(1.12\right)^t$

• $200\cdot\left(\left(1.06\right)^2\right)^t$

• $200\cdot\left(1.06\right)^t$

• $200\cdot\left(\left(.06\right)^2\right)^t$

Evaluating Functions

• Type the function into the desmos calculator on line 1

• On line 2, type what value you are inputting for x

• The output or answer is then given to you!

Multiple Choice

The following function represents the value of a car t years after it is purchased.

 $f\left(t\right)=12000\cdot\left(.85\right)^t$  
If the car was purchased in 2010, how much was it worth in 2015?

• 5324.46

• 12000

• 10200

• 1048.25

Open Ended

What questions do you have?

Poll

How are you feeling about the test tomorrow?