Notes – Lesson 8.1
Algebra 2
Name __________________________
Examples for questions 1-8.
Graph each function. Set up tables on calculator.
1. y = 3(10)x
2. y = 9(3)X
Examples for questions 9 and 39.
1. Exponential Function: _____________________ where _________________________________________
2. a is the _________________________________ b is called the __________________________________________
3. You can use an exponential function to model population growth. If you know the rate of increase r, you can find the growth
factor by using the equation
or rate of decrease
______________________________
_________________
Example:
A new car sells for $18,000 depreciates 25% each year. Write a function that models the value of the car. Find the value of the
car after 4 yr.
The bear population increases at a rate of 2% per year. There are 1573 bear this year. Write a function that models the bear
population. How many bears will there be in 10 yr?
The population of an endangered bird is decreasing at a rate of 0.75% per year. There are currently about 200,000 of these birds.
Write a function that models the bird population. How may birds will there be in 100yr?
Examples for questions 10-15.
Writing an Exponential Function
1. Write an exponential function y = ab x for a graph that includes (2, 2) and (3, 4).
y = abx
y = abx
Use your equation for a
Substitute (2, 2)
Substitute (3, 4)
Solve for a.
Plug in a.
Plug in b.
Simplify
Simplify
Solve for b.
2. (4, 8), (6, 32)
3. (2, 18), (5, 60.75)
Examples for questions 16-23.
Graph y = 14(.95)x growth or decay? ________________
Rule:
if b > 1 ________________________________,
y = 5(1.05)x growth or decay? ________________
if 0 < b < 1 ______________________________
Growth or Decay?
y = 100(0.12)x __________________--
y = 0.5(5)x __________________
Examples for questions 36-41.
For each function, find the annual percent increase or decrease that the function models.
2. y = 30.69( 85 ) x
1. y = 1700(0.75)x
3. y = 984.5(1.73)x
Examples for questions 46 – 53.
1. +45%
2. -10%
3. -40%
4. -200%
Examples for questions 35.
Suppose you want to buy a used car that costs $11,800. the expected depreciation of the car is 20% per year. Estimate the
depreciated value of the car after 6 years.
Assignment
Page 434: 1-31(odd), 35, 36-41(all), 46-53(all)