Key Features Expon. f(x)'s
Growth or Decay
Growth or Decay 2
Percent Rate
Transformations
100
If, y=a(bx ), what do they represent?
a = initial amount/y-intercept
b = growth/decay factor
100
Is the following function growth or decay:
f(x)=7(3/2)^(x-2)
Growth
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 growth factor?
initial population = 10
growth rate = 2
100
What is the percent growth/decay rate?
y=5(0.5)^x
decay by 50%
100
In an exponential function, what happens when h is a negative number?
f(x)=-a(b)x-h+k
The graph shifts right "h" units
200
What is the initial value and growth/decay factor for the function f(x) = 2(3)x
**Make sure to identify whether it is growing or decaying**
initial value = 2
GROWTH FACTOR = 3
200
What percentage growth 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
Create an exponential function that reflects over the x-axis and has an asymptote at y=-3.
-(2)^(x+5)-3
300
What is the equation for this exponential function.
y = 1(2)x
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 rate?
y=(0.01)^x
decay by 99%
300
List the transformations in the following exponential function:
f(x)= -1/3(7)^(x+5)-1
Reflection over the x-axis
Vertical shrink by 1/3
Shift left 5 units
Shift down 1 unit
400
What is the equation for the function?
y = 5(2)x
400
What percentage growth does the following equation represent?
y = 4(3)x
200%
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 by 30%
400
Create an exponential function that has a vertical stretch, shifts right three units, and shifts up four units.
f(x)=7(6)^(x-3)+4
500
What is the difference between linear functions and exponential functions?
Linear has a constant rate of change.
Exponential has a FACTOR.
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
growth by 33%
500
If g(x) is a transformation of f(x), then what transformations occur?
f(x) = bx
g(x) = 3f(x)+4
Vertical stretch of 3 units
Shift up 4 units