Unit 4 Exponential Functions

What kind of function?

100

Fill in the blank:
Exponential functions have a ______.

Common factor.

(Remember: a factor is a number that multiplies with another number)

200

Fill in the blank:
Linear functions have a __________.

Common Difference

(Adding the same amount each time)

300

Fill in the blank:
Quadratic functions have a ______.

A second common difference.

      2       2     2       2

      ^      ^     ^      ^

   7     9      11    13     15

  ^     ^      ^      ^      ^ 

1    8     17     28     41    56

400

What are the other names for the following sequence types:

arithmetic

geometric

arithmetic = linear

geometric = exponential

Write that equation!

100

^{Write the exponential equation for the following table:}

x        y

-1     4/3

0       4

1      12

2      36

3      108

f(x) = 4(3)^x

200

Write the exponential equation for the following table:

x        y

-1     12

0       4

1      4/3

2      4/9

3      4/27

f(x) = 4(1/3)^x

300

Write the exponential equation for the following scenario:
The value of a famous painting will increase each year by 4.5%. The original value was $15,250.

y = 15250(1 + 0.045)^x

y = 15250(1.045)^x

y = new value of painting

x = number of years

400

Write the exponential equation for the following scenario:
A faucet to a water tank is leaking 3% of the water every hour. The tank had 24 gallons in it before the leak occurred. 

y = 24(1 - 0.03)^x

y = 24(0.97)^x

y = new amount of water in the tank

x = number of hours

Write that equation! Word Problem Edition

100

Solve the following:
A population of barn owls is doubling each year. When measured in 2011, there were 381 owls. How many owls will there be in 2018?

y = 381(2)⁷

y = 48768

200

Solve the following:
The value of a car depreciates by 12% every year. What is the value of a $24,000 car after 5 years?

y = 24000(1 - 0.12)⁵

y = 24000(0.88)⁵

y = 12665.57

300

Solve the following:
An investment account has a 7% annual interest rate. If you invest $2,300, what is the value of the account after 12 years?

y = 2300(1 + 0.07)^x

y = 2300(1.07)¹²​

y = $5180.04

​​​

400

Solve the following:
A credit card has a 2.8% annual interest rate that is being compounded monthly. If you made $650 worth of purchases on the card, how much will you owe after 7 years?

y = 650(1 + 0.028/12)^12*7

y = $790.56

Calculating Inputs

100

Solve the following:
f(x)=3(6)x        f(4)= ?

f(4) = 3(6)⁴

f(4) = 3888

200

Solve the following:
f(x)=5(2/3)^x        f(6)= ?

f(6) = 5(2/3)⁶

f(6) = 0.44

300

Create a table for the following equation:

y = 2(3.5)^x

x       y

0

1

2

3

x     y

0     2

1     7

2     24.5

3     85.75

400

Create a table for the following equation:

y = 500(0.25)^x

x       y

0

1

2

3

x       y

0      500

1      125

2      31.25

3      7.81

Percent Increase / Decrease

100

Something is 45% more than the original amount.  What number would we multiply with?

1.45

100% + 45% = 145%

145% --> 1.45

200

Something loses 92% of it's original value.  What number would we multiply with?

0.08

100% - 92% = 8% remaining

8% --> 0.08

300

The rookie card of Shai Gilgeous-Alexander has increased in value by 97%. It was originally valued at $2200.  How would the new value be calculated in one step?

2200(1.97)

100% + 97% = 197%

197% --> 1.97

400

1980's memorabilia has been having a tough year.  Vintage items have decreased in value by 14%.  Ms. Cooper's Garbage Pail Kids collection was worth $1572 last year.  How would the new value be calculated (in one step)?

1572(0.86)

100% - 14% = 86%

86% --> 0.86