1. Exponential Growth and Decay Real World Applications

2. Exponential Growth y = a(1 + r) t a → initial amount r → percent increase 1 + r → growth factor t → time in years

3. Exponential Decay y = a(1 - r) t a → initial amount r → percent decrease 1 - r → decay factor t → time in years

4. 1. Identify the initial price of the house, the growth factor, and the annual increase given P = 120000(1.13) t 2. Identify the initial cost of the car, the decay factor, and annual decrease given V = 25000(0.8) t

5. Steps to Solve 1.Decide if it is exponential growth or decay 2.State what a, r, and t are equal to 3.Write the model and calculate 4.Answer the question

6. Tuition Cost In 1990, the cost of college tuition was an average of $4,300. Over the next 8 years, tuition rose 4%. a)Write a model to describe the rise in tuition in terms of t, years. b)Determine the cost of tuition in 2010.

7. Car Depreciation A new car costs $23,000. The value of the particular car will depreciate by 15% each year. a)Write a model to describe the price of the car in terms of t years. b)Use the model to estimate the value of the car in 3 years. c)Predict when the value will be half of the original price.

8. Computer Cost You buy a new computer for $2100. The value of the computer decreases by about 50% annually. a)Write a model for the value of the computer. b)Use the model to determine the value of the computer after 2 years.

9. Land Value You have inherited land that was purchased for $30,000 in 1960. The value V of the land increased by approximately 5% per year. a)Write a model for the value of the land t years after 1960. b)What is the approximate value of the land this year, 2009?

10. Compound Interest A = P(1 + r/n) nt A → Amount of Money P → Principle r → Rate n → Number of Times per Year t → Time in Years

11. Vocabulary Compounded Annually: _____________ Compounded Biannually: _____________ Compounded Quarterly: ______________ Compounded Monthly: _______________

12. Sally wants to start saving money. She deposits $150. into a savings account at a 7.5% annually interest. Find how much money will be in her account in 3 years if the interest is compounded a)Annually b)Quarterly c)Monthly

13. Car Depreciation A new car costs $15,000. The value of the particular car will depreciate by 10% each year. a)Write a model to describe the price of the car in terms of t years. b)Use the model to estimate the value of the car in 3 years.

14. 2. Define each of the following terms a. Compounded quarterly b. Compounded monthly c. Compounded annually

15. Savings Account You would like to start saving money for a car. You decide to deposit $500 into a savings account at a 8% annual interest rate compounded monthly. a)Write a model to describe the amount of money, m in your account in terms of t years. b)Complete the table below. Describe what one of the ordered pairs mean in respect to the problem. c)Predict when you will have saved at least $1000. t12345 m