Key Features Expon. f(x)'s
Growth or Decay
Growth or Decay
Percent Rate
Word Problems
100
If, y = a(bx), What are the parameters (a & b) and what do they represent?
a = initial amount/y-intercept
b = factor
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
A bunny population doubles every 6 months. If the starting population is 10, what is the y-intercept of the graph? What is the growth factor?
y-intercept = (0,10)
growth factor= 2
100
What is the percent growth/decay?
y=50(.5)x
Decay, 50%
100
2243
200
Why is a linear function a straight line, and an exponential function a curve?
Linear functions have a constant rate of change, exponential functions have a changing rate of change.
200
What are two guaranteed points on the graph of y=4(2)x?
(0,4) and (1,8)
(remember, when x=0, y=a; when x=1, y= a(b) )
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
30%
200
What will be the cost in 17 years?
$32,313.27
300
What is the y-intercept and horizontal asymptote?
y-intercept = (0, 1)
asymptote (boundary): y=0
300
f(x)=a(.93)x
Does this functions represent exponential growth or decay? What is the percent growth/decay rate?
Exponential Decay
r = 7%
300
f(x)=37(1.07)x
Does this function represent exponential growth or decay? What's the factor?
Exponential Growth.
Factor: 1.07
The rate would be 7%
300
What is the percent growth/decay rate?
y=(0.01)^x
99%
300
16,941 people
400
What's the factor?
b=2
400
Label the following formula:
y = final amount
a = initial amount
r = rate of growth
t = time
400
Does the graph represent exponential growth or decay?
Exponential Growth
400
Is this exponential growth or decay?
What is the percent growth/decay rate?
y=1/2(0.7)^x
Decay. 30%
400
You buy a car for $15,000 that depreciates at a rate of 8% annually. How many years will it take for your car to lose HALF its value? (In other words, be worth less than $7500)
After 8 years, the car's value is $7698 (still above $7500).
After 9 years, the value is $7082. It will take 9 years for the car to lose half its value.
15000(1-.08)9=7082
500
What is the difference between linear functions and Exponential functions?
Linear has a common difference
Exponential has a common multiplier
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
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 percent growth/decay rate?
y=60(1.33)^x
33%
500
You put $500.00 into an account that earns 3% interest annually. If you do not deposit any other money into the account, how many years will it take for your account to be over $750?
500(1+.03)14=756.29
It will take 14 years for the account to be over $750.