Exponential Vocabulary
Growth or Decay
Equations
Growth or Decay
Word Problems
Rate
Mixed Bag of Conversions
100
If, y=a(b)x, What do a and b represent?
a=initial amount/y-intercept
b=(common ratio)(growth or decay factor)
100
y=2(0.93)x
Does this functions represent exponential growth or decay?
Exponential Decay
100
Write the exponential equation:
Initial Amount= 550
Decay FACTOR = (0.67)
y=550(0.67)x
100
In exponential functions, when b>1 this will cause an exponential growth or decay?
Exponential growth
100
y=2300 (0.995)x
model enrollment at Cary High, where x is the number of years after 2020. What will the enrollment be in 2030?
2243 students
100
y =5(1.07)x
Does this functions represent exponential growth or decay?
What's the percent growth/decay factor?
Exponential Growth. 7%.
100
Growth Rate = 20%
What is the decimal?
What is the growth factor?
Decimal = 0.2
Growth Factor = (1.2)
200
Which number is the y-intercept and which is the growth factor for the function f(x)=2(3)x
y-intercept=2
growth factor= 3
200
Do the following equations represent exponential growth, decay, or neither?
a) y=3.5(0.3)x
b) y=2(3)x
c) y=5x+6
a) Decay
b) Growth
c) Neither (It's linear! y=mx+b)
200
The population of rabbits doubles every 6 months. If there are initially 100 rabbits, how many will there be after 2 years?
y=100(2)4 = 1600 rabbits
200
A bunny population doubles every year. If the starting population is 10, write an exponential function to model the situation.
y = 10(2)x
200
The value of a smartphone depreciates at a rate of 15% per year. If the initial value is $1,000, find the smartphone's value after 3 years. Answer to the Hundredth
$614.125
200
What is the RATE of growth/decay in the following expression?
y = 1400(0.92)t
8% decay
200
Growth Rate= 9%
What is the decimal?
What is the growth factor?
Decimal= .09
Growth factor= (1.09)
300
What is the y-intercept for the graph below?
y=1(2)x
300
y = 4(0.7)x
What is the decay factor?
What is the decay rate?
0.7 decay FACTOR
30% decay RATE
300
Annual sales of a fast food restaurant are $530,000 and increasing at a rate of 5% per year. What will the annual sales be in 6 years? (show the equation and answer)
$710,250.69 annual sales.
300
What's the growth factor? (the b value in equation)
b=2
300
The population of a town is 18,000 and is decreasing at a rate of 2% per year. What is the population after 3 years?
16,941 people
300
Decay Rate = 37.5%
What is the decimal?
What is the decay factor?
decimal= .375
decay factor= 0.625
300
b = (0.07)
What is the percent?
What is the growth/ decay rate (as a percent)?
Percent= 7%
Decay Rate= 93%
400
Is the function exponential growth or decay? What is the b-value? 
Decay
b=1/2
400
A house is worth 9,000 dollars and the price increases by 20%. Which equation models the situation?
A) y = 9,000 (0.8)x
B) y = 9,000 (1+.02)x
C) y = 9,000 (1.02)x
D) y = 9,000 (1.2)x
D) y = 9,000 (1.2)x
400
Does the graph represent exponential growth or decay?
Exponential Growth
400
If Abby bought some cryto coins for $120. The value of the coins increases at a rate of 9% per year. How much are the coins worth in 6 years?
$201.25
400
f(x)=5(1.97)x
Does this function represent exponential growth or decay? What is the growth/decay RATE
Exponential Growth
Rate: 0.97 or 97%
400
Decay Rate = 15%
What is the decimal?
What is the decay factor?
Decimal= 0.15
Decay factor= (0.85)
500
All of the following indicate exponential decay EXCEPT which term?
decrease
depreciate
deposit
decay
deposit
500
y = 115 ∙ (0.42)x
Initial Amount= _____
Growth or Decay FACTOR = ______
Growth or Decay RATE = _____
Initial Amount= 115
Growth or Decay FACTOR = 0.42
Growth or Decay RATE = 58%
500
Write the equation given the initial amount and the growth or decay rate.
Initial: 430
25% decay
y = 430 (0.75)x
500
Annual sales of a fast food restaurant are $530,000 and increasing at a rate of 5%. Write an exponential function to model the situation.
y = 530,000(1.05)x
500
The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year
What will be the cost in 17 years?
$32,313.27
500
Mrs. Renaud purchased a car for 26,400 and every year it depreciates by 12%. Write an exponential function to model the situation.
y = 26,400(0.88)x
500
Growth rate= 1.145
What is the percent?
What is the decimal?
Percent=14.5%
Decimal=.145