1. Introduction to Exponential Functions
Growth/Decay
Transformation
Geometric Sequence

2. M&M Investigation Lap Handout Lab direction Materials Need: M&M’s Cup
Napkin
Lab Instruction/Question Worksheet

3. Investigation Discussion:
What did you notice about your scatter plot?
Is it possible to have zero value?
Is it possible for these situation to be
Linear?
Quadratic?

4. Graph: 𝑦= 5 𝑥

5. Graph: 𝑦= 𝑥

6. What do you know?
The two functions I just graphed are ___________________ functions. Exponential functions are equations in the form of ______________ where ________ and ________ are greater than zero. When the value of b is greater than 1, the graph of the function will ________________ from left to right. This is also known as exponential ______________. When the value of b is greater than zero but less than 1, the graph of the function will ______________ from left to right. This is also known as exponential _____________. The value of a is always the _______________ value or the _____________ amount.
𝑦=𝑎∙ 𝑏 𝑥 or 𝑦=𝑎 𝑏 𝑥

7. Circle the initial amount and put a box around the growth/decay factor
Circle the initial amount and put a box around the growth/decay factor. Then determine if the problem represents growth or decay and if the graph will be increasing or decreasing.
1) y=3∙ 1.3 x 2) y=5000∙ 0.93 x
3) y= x 4) y=10∙ x
5) y=120000∙ 0.85 x 6) y= x

8. Growth Keywords:
Increase Up
Appreciate

9. Decay Keywords:
Decrease
Going Down
Depreciate

10. To Determine the Rate or “b” (when it isn’t provided for you):
Change Percent to a Decimal
Growth: decimal
Decay: – decimal
Put this value into the equation for “b”
Ex: increase by 12% Ex: decrease by 9%

11. Rewrite the following statements into the b-value that would be used in the equation.
1) increase by 3.5%
2) decrease by 6%
3) increase by 0.25%
4) decrease by 4.75%

12. Given the equation y = 35(0.57)x
a) Does this equation represent growth or decay? _______________ b) What is the rate of growth or decay? _______________ c) What is the initial value? _______________ d) Evaluate for x = 5 _______________

13. Given the equation y = 225(1.23)x
a) Does this equation represent growth or decay? _______________
b) What is the rate of growth or decay? _______________
c) What is the initial value? _______________
d) Evaluate for x = _______________

14. Given the equation y = 154(1.06)x
a) Does this equation represent growth or decay? _______________
b) What is the rate of growth or decay? _______________
c) What is the initial value? _______________
d) Evaluate for x = _______________

15. Example 1:
Raymond invested $4,000 in a new company. The value of his investment has been growing at a rate of 6% per year for the last 5 years. The function 𝐴=4, 𝑡 represents the growth of his investment of $4,000, where A is the total value of his investment and t is the time invested in years. What is the total value of his investment after 5 years?
Circle one: Growth or Decay
Rate:
Initial Amount:

16. Example 2:
The value of a new car decreases as soon as it is driven off the dealer’s lot. The function 𝑉=30, 𝑡 models the depreciation of the value of a new car that originally cost $30,000, at a yearly decrease of 18%, where V is the value of the car and t is the time in years from the time the car was purchased. What is the value of the car after 3 years?
Circle one: Growth or Decay
Rate:
Initial Amount: