1. Section 7.6 Day 1 Exponential Growth & Decay
Algebra 1

2. Compounded Interest Equation
𝐴=𝑃 1+ 𝑟 𝑛 𝑛𝑡
Time
r: interest rate
n: number of times interest is compounded each year
Initial Amount

3. Terminology
Annually : Once a year Semi-annually: twice a year Quarterly: 4 times a year Monthly: 12 times a year Weekly: 52 times a year

4. Example 1
Maria’s parents invested $14,000 at 6% per year compounded monthly. How much money will there be in the account after 10 years?
P: 14,000
R: 0.06
T: 10
N: 12
About 25,

5. Example 2
You invest $700 into an account with 3.5% interest for 20 years. Make a chart to calculate the following. Then, write a sentence on the results.
Compounded annually
Compounded semi-annually
Compounded quarterly
Compounded monthly
Compounded weekly

6. Example 2 Compounded annually Compounded semi-annually
𝐴= =
Compounded semi-annually
𝐴= =
Compounded quarterly
𝐴= =
Compounded monthly
𝐴= =
Compounded weekly
𝐴= =

7. Exponential Growth General Equation
Exponential Growth Equation:
𝑦=𝑎 1+𝑟 𝑡
Time
Rate of Change (in decimal)
Initial Amount

8. Exponential Decay General Equation
Exponential Decay Equation:
𝑦=𝑎 1−𝑟 𝑡
Time
Rate of Change (in decimal)
Initial Amount

9. Exponential Growth: Example 1 PG 432 EX 1
The prize for a radio station contest begins with a $100 gift card. Once a day, a name is announced. The person has 15 minutes to call or the prize increase by 2.5% for the next day.
A) What is the initial amount?
B) What is the rate of change in a decimal?
C) What is the time?
D) What is the equation representing this situation?
E) How much will the gift card be worth if no one wins after 10 days?

10. Exponential Growth: Example 1 Answers
A) What is the initial amount?
$100
B) What is the rate of change in a decimal?
0.025
C) What is the time? t
D) What is the equation representing this situation?
𝑦= 𝑡
E) How much will the gift card be worth if no one wins after 10 days?
𝑦= =$128.01

11. Exponential Decay: Example 2 PG 433 EX 3
A fully inflated child’s raft for a pool is losing 6.6% of its air every day. The raft originally contained 4500 cubic inches of air.
A) What is the initial amount?
B) What is the rate of change in a decimal?
C) What is the time?
D) What is the equation representing this situation?
E) Estimate the amount of air in the raft after 7 days

12. Exponential Decay: Example 2 Answers
A) What is the initial amount?
4500 cubic inches
B) What is the rate of change in a decimal?
0.066
C) What is the time? t
D) What is the equation representing this situation?
𝑦= − 𝑡
E) Estimate the amount of air in the raft after 7 days
𝑦= − = 𝑐𝑢𝑏𝑖𝑐 𝑖𝑛𝑐ℎ𝑒𝑠

13. Example 3
In 2000, 2200 students attended Polaris High School. The enrollment has been declining 2% annually. How many students will be enrolled in 2015?

14. Example 3- Answer
In 2000, 2200 students attended Polaris High School. The enrollment has been declining 2% annually. How many students will be enrolled in 2015?
𝑦= − =1624 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠

15. Sage & Scribe Find one partner
Decide who is going to be person 1 and who is going to be person 2
Indicate that on your piece of paper and write your name down
This will be collected for classwork points!

16. Partner 1:
Partner 1: You are the Sage. You need to verbally explain how to solve the problem step by step. You CANNOT write anything
Partner 2: You are the scribe. You CANNOT say anything and can ONLY write down EXACTLY what the Sage tells you to write down.

17. Example 4
Ms. Acosta received a job as a teacher with a starting salary of $34,000. According to her contract, she will receive a 1.5% increase in her salary every year. How much will Ms. Acosta earn in 7 years?

18. Example 4 - Answer
Ms. Acosta received a job as a teacher with a starting salary of $34,000. According to her contract, she will receive a 1.5% increase in her salary every year. How much will Ms. Acosta earn in 7 years?
𝑦=34, =$

19. Partner 2:
Partner 2: You are the Sage. You need to verbally explain how to solve the problem step by step. You CANNOT write anything
Partner 1: You are the scribe. You CANNOT say anything and can ONLY write down EXACTLY what the Sage tells you to write down.

20. Example 5
The Work-Out Gym sold 550 memberships in Since then, the number of memberships sold has increased 3% annually. If this trend continues, predict how many memberships the gym will sell in 2020.

21. Example 5 - Answer
The Work-Out Gym sold 550 memberships in Since then, the number of memberships sold has increased 3% annually. If this trend continues, predict how many memberships the gym will sell in 2020.
𝑦= =9644 𝑚𝑒𝑚𝑏𝑒𝑟𝑠ℎ𝑖𝑝𝑠