Math 3 Day 5 Exponential Functions
An exponential function is a function in the general form ______
where ______
a =______b = ______
x = ______Growth/Decay as a Factor:
Growth/Decay as a Percentage:
Growth Decay
b > 1 0 < b < 1
Graph the following in your calculator and draw a quick sketch of what you see. What’s happening?
1. y = 1(2)x 2. y = 1(5)x 3. y = 1(15)x
4. y = 1(.8)x 5. y = 1(.5)x 6. y = 1(.1)x
Does the exponential function imply growth or decay? By what percentage?
1. y = 67(1.06)x 2. y = -98(.87)x
3. y = 300(1.27)x 4. y = 142(.35)x 5. y = 5(2)x
Word Problems:
1. Suppose 20 rabbits are taken to an island. The rabbit population then triples every year. The function f(x) = 20 • 3x where x is the number of years, models this situation.
a) What does “a” represent in this problem? b) What does “b” represent in this problem?
c) How many rabbits would there be after 2 years?
2. Suppose two mice live in a barn. If the number of mice quadruples every 3 months, how many mice will be in the barn after 2 years?
3. The value of an iPad decreases at 35% per year. If the starting price of the iPad is $500, write the exponential function
b) How much will the iPad be worth after 5 years? c) When can you buy the iPad for $5?
4. Suppose the acreage of forest is decreasing by 2% per year because of development. If there are currently 4,500,000 acres of forest, how much forest will there be in 6 years?
5. Find a bank account balance to the nearest dollar, if the account starts with $100, has an annual interest rate of 4%, and the money is left in the account for 12 years.
b) If you wanted to buy a new gaming system for $250, when will you have enough?
Half-Life: Some unstable substances, like plutonium, decay over time. To measure the rate of decay, scientists refer to their “half life.” The half life is the ______
______.
6. The pesticide DDT was widely used in the United States until its ban in 1972. Write an equation that models the 15 year half-life of 100 grams of DDT.
b) How much DDT would be remaining after 45 years?