Key Features
Growth or Decay
Equations From Two Points
Percent Rate
Word Problems
100
If, y=a(b)x, What do the a and b represent?
a=initial amount/y-intercept
b=multiplier
100
How do I know if an exponential function is exponential decay from an equation?
If the b is in between 0 and 1
100
Write an exponential function that goes through the two points: (0, 5) and (1, 35)
y = 5(7)x
100
What is the percent growth/decay rate?
y=5(0.5)^x
50%
100
2243
200
What is the y-intercept and multiplier for the function f(x)=2(3)x
y-intercept=2
growth factor= 3
200
f(x)=.25(1.3)x
Does this functions represent exponential growth or decay? What is the percent growth/decay rate?
Exponential Growth
30%
200
Write an exponential function that goes through the two points: (0, 16) and (3, 128)
y = 16(2)x
200
What is the percent growth/decay rate?
y=5(1.3)^x
30%
200
What will be the cost in 17 years?
$32,313.27
300
What is the y-intercept and multiplier?
y-intercept = (0, 5)
Multiplier = 2
300
f(x)=a(.93)x
Does this functions represent exponential growth or decay? What is the percent growth/decay rate?
Exponential Decay
7%
300
Find the multiplier for the exponential function passing through: (-1, 2) and (2, 84)
b = 3.48
300
What is the percent growth/decay rate?
y=(0.01)^x
99%
300
16,941 people
400
What's the multiplier? What is the y-intercept?
a = 1
b = 2
400
Mr. Medina purchased a car for 26,400 and every year it decays by 12%. What can he expect the value of his car to be after 3.5 years?
f(x)=26400(.88)3.5=$16,876.92
400
Find the multiplier for the exponential function passing through the points: (2, 16) and (12, 42)
b = 1.10
400
Is this exponential growth or decay?
What is the percent growth/decay rate?
y=1/2(0.7)^x
Decay. 30%
400
Annual sales of a fast food restaurant are $530,000 and increasing at a rate of 5%. What will the annual sales be in 6 years?
530,000(1.05)6 =$710,250.69
500
What is the difference between linear functions and Exponential functions
Linear has a constant difference
Exponential has a multiplier
500
A bunny population doubles every 6 months. If the starting population is 10, how many will you have after 2 years?
Two years population: 160
500
Write an exponential function that goes through the two points: (2, 18) and (4, 55)
(You should get decimals)
y = 5.89(1.75)x
500
If you start with $200 and end up with $160 after a month, find the multiplier you would use to create an equation, then find the percent change.
multiplier: .80
20% change
500
If you put $500 into an account and the account earns 3% interest after every six months. How much will be in the account after 5 years?
$671.96