1. 7.1 Growth and Decay

2. An exponential equation has the general form
7.1 Exponential Growth and Decay
An exponential equation has the general form
y=abx

3. Given the general form: y=abx
7.1 Exponential Growth and Decay
Given the general form: y=abx
When b > 1, b is the growth factor
When 0 < b < 1, b is the decay factor
Such a situation is called  Exponential Growth.
Such a situation is called  Exponential Decay.

4. Growth or Decay???
Growth
Decay
Growth
Decay
Growth
Decay

5. 7.1 Exponential Growth and Decay
Many real world phenomena can be modeled by functions that describe how things grow or decay as time passes.  Examples of such phenomena include the studies of populations, bacteria, the AIDS virus, radioactive substances, electricity, temperatures and credit payments, to mention a few.

6. exponential growth exponential decay. Growth: Decay:
7.1 Exponential Growth and Decay
Any quantity that grows or decays by a fixed percent at regular intervals is said to possess
exponential growth 
or 
exponential decay.
Growth:
y = a(1+r)x
Decay:
y = a(1 – r)x
a = initial amount before measuring growth/decay
r = growth/decay rate (often a percent) -> (rate = b-1)
x = number of time intervals that have passed

7. Growth or Decay??? Rate = b-1 Growth Growth Rate: 0.2 or 20% Decay
Decay Rate: 0.1 or 10%
Growth
Growth Rate: 0.54 or 54%
Decay
Decay Rate: 0.3 or 30%
Growth
Growth Rate: 1.0 or 100%
Decay
Decay Rate: 0.93 or 93%

8. A certain car depreciates about 15% each year.
Example 1:
A certain car depreciates about 15% each year.
a. Write a function to model the depreciation in value for a car valued at $20,000.
____________________
b. Graph the function.
c. Suppose the car was worth $20,000 in What is the first year that the value of this car will be worth less than half of that value?
_________________

9. Example 2:
Some real estate agents estimate that the value of a house could increase about 4% each year.
a. Write a function to model the growth in value for a house valued at $100,000.
____________________
b. Graph the function.
c. A house is valued at $100,000 in Predict the year its value will be at least $130,000.
_________________

10. Example 3:
Colleen’s station wagon is depreciating at a rate of 9% per year. She paid $24,500 for it in What will the car be worth in 2008 to the nearest hundred dollars? __________________________

11. Example 4:
Kyle estimates that his business is growing at a rate of 5% per year. His profits in 2005 were $67,000. Estimate his profits for 2010 to the nearest hundred dollars. __________________________

12. Example 5:
A parcel of land Jason bought in 2000 for $100,000 is appreciating in value at a rate of about 4% each year.
a. Write a function to model the appreciation of the value of the land.
____________________
b. Graph the function.
c. In what year will the land double its value?
_________________