1. Exponential Functions
Pre-calculus Unit 3

2. Exponential growth
When have you seen exponential growth in a real-world situation?
What are some properties of exponential growth functions?
Domain/range, intercepts, continuity, end behavior, etc.

3. Exponential decay
When have you seen exponential Decay in a real-world situation?
What are some properties of exponential decay functions?
Domain/range, intercepts, continuity, end behavior, etc.

4. Exponential Growth and Decay
Exponential growth and decay Formula:
𝑁= 𝑁 0 (1+𝑟) 𝑡
Where N˳ is the initial amount
R is the growth rate if r > 0
R is the decay rate if R < 0
T is the Amount of time

5. Exponential Growth and Decay
Continuous Exponential growth and decay Formula:
𝑁= 𝑁 0 𝑒 𝑘𝑡
Where N˳ is the initial amount
K is the continuous growth rate, then K > 0
K is the continuous decay rate, then k < 0
T is the Amount of time

6. Growth or Decay
Mexico has a population of approximately 110 million people. If mexico’ s population continues to grow at the described rate, predict the population of Mexico in 10 and 20 years.
If growth rate is 1.42% annually
If growth rate is 1.42% continuously

7. Growth or Decay
The population of a town is Declining at a rate of 6%. If the current population is 12,426 people, predict the population in 5 and 10 years using:
Annually
Continuously

8. Examples
Jasmine receives a 3.5% raise at the end of each year from her employer to account for inflation. When she started working for the company in 1994, she was earning a salary of $31,000.
What was jasmines salary in 2000? 2009?
What will it be in 2024?

9. Examples
The half-life of a radioactive substance is the amount of time it takes for half of the atoms of the substance to disintegrate. Uranium-235 is used to fuel a commercial power plant. Its half-life is 704 million years.
How many grams of uranium will remain after 1 million years if you start with 200 grams?

10. Examples
Under the right growing conditions a particular species of plant has a doubling time of 12 days. Suppose a pasture contains 46 plants of this species. How many plants will their be after 20, 65, and x days?

11. True or false
Exponential functions can never have restrictions on the domain.
Exponential functions always have restrictions on the range
Graphs of exponential functions always have an asymptote.

12. Extra Practice
Worksheet

13. M&M Activity
Follow the directions on the worksheet.

14. Compound interest

15. Compound interest Formula: A 𝑡 = 𝑃 (1+ 𝑟 𝑛 ) 𝑛𝑡
Where p = initial amount invested, r = interest rate, t = time

16. Compound interest Continuous Compound Formula: 𝐴=𝑃 𝑒 𝑟𝑡
Used only when doing compounded daily!

17. Compound interest What are the different types of compounding?
Annually
Semi-Annually
Quarterly
Monthly
Weekly
Daily

18. Compound interest
If I invested $500 into an account which yields 5% annual interest, how much would I have after 7 years if the interest was compounded
Annually
Quarterly
Daily

19. Compound interest
Krysti invests $1200 in an account with a 6% interest rate, making no other deposits or withdrawls. What will Krysit’s account balance be after 20 years if the interest is compounded:
Semi-Annually
Monthly
Daily

20. Compound Interest Which should I invest $1200 in?
A 3 year CD with 3.45% interest compounded continuously
A 5 year cd with 4.75% interest compounded monthly?