Key Features Expon. f(x)'s
Growth or Decay
Growth or Decay 2
Percent Rate
Linear vs. Exponential
100
If, y=a(bx ), what do a and b represent?
a = initial amount/y-intercept
b = growth/decay factor
100
How do I know if an exponential function is exponential decay from an equation?
If the b is less than 1.
100
A bunny population doubles every 6 months. If the starting population is 10, how many will you have after 3 years? What is the initial population? What is the constant ratio?
after 3 years = 640
initial population = 10
Constant Ratio = 2
100
What is the percent growth/decay rate?
y=5(0.5)^x
decay by 50%
100
What is the difference between linear functions and exponential functions?
Linear has a constant rate of change (slope).
Exponential functions increase or decrease at a constant ratio (multiplying, exponent=variable)
200
What is the initial value and rate of growth/decay for the function f(x) = 2(3)x
**Make sure to identify whether it is growing or decaying**
initial value = 2
Growth Rate = 200%
200
What growth RATE does this equation represent?
y = 3(1.5)x
50%
200
In exponential functions, when b>1 this will cause an exponential growth or decay?
Exponential growth
200
What is the percent growth/decay rate?
y=5(1.3)^x
growth by 30%
200
What type of function does this graph represent? Why? 
Exponential - curve with a horizontal asymptote
300
Is this a graph of an exponential function? How do you know? 
Yes - it curves and has a horizontal asymptote.
300
f(x)=a(.93)x
Does this functions represent exponential growth or decay? What is the percent growth/decay RATE?
Exponential Decay by 7%
300
f(x)=a(1.07)x
Does this functions represent exponential growth or decay? What's the percent growth/decay rate?
Exponential Growth. 7%.
300
What is the percent growth/decay FACTOR?
y=(0.01)^x
decay by 1%
300
Which scenario does not represent an exponential function?
1) The population of bacteria quadruples every hour.
2) The value of a cell phone depreciates at a rate of 5.75% each year.
3) A baseball tournament eliminates half of the teams after each round.
4) A water park allows 100 people in every 45 minutes.
Option 4
400
The equation V(t)=15,000(0.65)t represents the value of a pontoon boat t years after it was purchased. Which statement is true?
1) The pontoon's value is decreasing at a rate of 65% each year.
2) The pontoon's value is decreasing at a rate of .35% each year.
3) The pontoon cost $9,750 when purchased.
4) The pontoon cost $15,000 when purchased.
Option 4: Starting value is $15,000
400
Laura invested $5000 in an account with a 2.7% annual interest rate. She made no deposits or withdrawals on the account for 5 years. If interest was compounded annually, which equation represents the balance in the account after 5 years?
1) A=5000(1-0.027)5
2) A=5000(1-2.7)5
3) A=5000(1+0.027)5
4) A=5000(1+2.7)5
Option 3
A=5000(1+0.027)5
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
400
Is this exponential growth or decay?
What is the percent growth/decay rate?
y=1/2(0.7)^x
Decay by 30%
400
Does the table represent a linear or exponential function? What is the constant rate or constant ratio?
Exponential - constant ratio of 2
500
The number of carbon atoms in a fossil is given by the function y=4700(0.9)x, where x represents the number of years since being discovered. What is the percent of change each year? Explain how you arrived at your answer.
10% decay each year.
Subtract 1 from the base (0.9-1=-0.1)
Multiply by 100 to get the percent (0.1x100=10%)
500
Ms. Wiggins purchased a car for 26,400 and every year it decays by 12%. What can she expect the value of her car to be after 3.5 years?
f(x) = 26400(.88)3.5 = $16,876.92
500
Marvin has his money invested in a mutual fund. The value, v(x), of his fund can be modeled with the function v(x)=50,000(0.82)x, where x is the number of years since he made his investment. Which statement describes the rate of change of the value of his portfolio?
1) It increases 82% per year
2) It increases 18% per year.
3) It decreases 82% per year.
4) It decreases 18% per year.
Option 2 - 18% decay rate
500
What is the percent growth/decay rate?
y=60(1.33)^x
growth by 33%
500
Which scenario represents exponential growth?
1) A swimming pool is filled at a rate of 50 gallons/minute
2) A bacteria doubles its population every 12 hours when the temperature is more than 75 degrees.
3) A plant grows 3 inches every week.
4) A train increases its distance from its home station as it travels at a constant speed of 40 miles per hour.
Option 2