Exponential Vocabulary
Growth or Decay
Equations
Growth and Decay
Word Problems
Rate
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
How do you know if this function represent exponential growth or decay?
Exponential Decay
The b value is between 0 and 1.
100
The function y = 12(3)x models an insect population after x weeks.
What will the population be after six weeks?
8,748 insects
100
In exponential functions, when b>1 this will cause an exponential growth or decay?
Exponential growth
100
A Petri dish contains 50 bacteria. The number of bacteria doubles every day.
a) What is the initial amount?
b) What is the growth factor?
c) Write the exponential equation that represents this scenario.
d) Now find the number of bacteria in the dish after 2 weeks.
a) 50
b) 2
c) y= 50(2)x
d) y= 50(2)14
819,200 bacteria
100
y = 45(1.07)x
Give the RATE as a % for this exponential function
Growth or Decay?
Exponential Growth. 7%.
200
Which number is the y-intercept and which is the growth factor for the function y=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
Write the exponential equation:
Initial Amount= 550
Decay FACTOR = 0.67
y=550(0.67)x
200
Does the graph represent exponential growth or decay?
Exponential Growth
200
You purchased a new computer for $1500. It decreases in value by about –18% each year. How much will your computer be worth in 6 years?
About $456
200
What is the RATE of growth or decay in the following expression?
y = 1400(0.92)5
8% decay
300
Name the y-intercept and write the equation for the graph below?
y-intercept: 1
growth factor: 2
y= 1(2)x
300
Is the function exponential growth or decay? What is the b-value? Write the equation. 
Decay
b=1/2
y=4,800(1/2)x
300
y= 2,300 (0.98)x
If this equation models enrollment at Cary High after 2020. What will the school enrollment be in 2030?
1879 students
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?
y= 18,000(0.98)3
16,941 people
300
What is the rate (the % increase or decrease) given the equation
y = 100 ∙ (0.75)x
A. 25% B. 75% C. 100% D. 175%
25% decrease
1 - .75 = .25
400
Arithmetic sequences are modeled by __________ functions.
Geometric sequences are modeled by ___________ functions.
linear
exponential
400
y = 4(0.7)x
What is the decay factor?
What is the decay rate?
0.7 decay FACTOR
30% decay RATE
400
Given equation: y = 80(1/2)x
Fill in the table:
(x, y)
(0, 80)
(1, 40)
(2, 20)
400
A colony of bacteria grows by 35% every hour. If the colony began with 100 bacteria, how many are there after 12 hours?
y= 100(1.35)12
3664.42 bacteria
400
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
400
y= 5(1.97)x
a. Does this function represent exponential growth or decay?
b. What is the growth/decay RATE
Exponential Growth
Rate: 0.97 or 97%
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 decay rate.
Initial: 230
40% decay
y = 230 (0.60)x
500
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)
y= 530,000 (1.05)x
$710,250.69 in annual sales.
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
Identify the initial amount, the growth factor and the percent growth rate. y = 12(1.23)x
initial amount: 12
growth factor: 1.23
rate: 23% growth