Exponential Functions
Graphing Exponential Functions
Exponential Growth and Decay
Compounded and Continuously Compounded Growth
100
This is what the "a" and "b" values are in
a(b)^x
What is the y-intercept (starting value) and base (multiplier)?
100
Sketch a graph of exponential growth. What is special about the multiplier when it’s growth?
What is 
100
A savings account earns 4% interest per year. If Josiah puts 500 dollars in now, this is how much will he have after 5 years
What is $608.33?
100
Given $1000 compounded quarterly at an annual 12% interest rate.
Write an equation to model this situation.
y = 1000(1+.12/4)^(4t)
200
This is the formula for exponential growth functions.
What is
a(1+r)^x
?
200
The graph of an exponential function will always cross the x - axis. True or false, explain your answer.
What is false.
200
The population of a small town is decreasing at a rate of 2% per year. in 1970 the population was 25,000. This is what the approximate population would be in the year 2020.
What is 9104?
200
Given $1600 compounded monthly at an annual 7% interest rate.
What is the initial value? What is n (# times compounded per year)?
Initial Value: $1600
N: 12 (12 months in a year)
300
These ordered pairs represent an exponential function; (-1, .5),(0,3),(1,18),(2,108). True or false, explain your answer.
True, there is a base (constant multiplier) of 6.
300
What is the base of the following function?
What are the transformations?
y = 4(2)^(x - 2) + 1
Base: 2x
Transformations:
1. Stretch of 4
2. Right 2
3. Up 1
300
The number of students in the book club is increasing at a rate of 15% per year and they started with 9 students. How much would they have after 7 years?
What is ~24 students?
300
y = Pe^(rt)
When do you use this equation? What does each variable stand for?
When you are using compounding continuously.
P - The initial value
e - The natural base, approximately 2.7
r - rate
t - time
400
This is the answer when f(x) = 10(5)^x is evaluated for f(3).
What is 1250?
400
Graph
y = 4(1/2)^x
400
Fluorine-20 has a half-life of 11 seconds. This is the amount of fluorine-20 left from a 50 gram sample after 44 seconds.
What is 3.125 grams?
400
Jasmine deposits $520 into a savings account that has a 3.5% interest rate compounded monthly. What will be the balance of Jasmine’s savings account after two years?
$557.65
500
The graph of an exponential function, V, passes through the points (0, 2) and (3, 128) as shown on the graph below. Write an equation for the function V(x).
What is
V(x) = 2(4)^x
500
Find the equation that models the following table.
What is
y = 3(2)^x
500
A new car that sells for $1800 depreciates 5% each year. How many years would it take for the car to only be worth $1000?
About 11.5 years
500
Jasmine deposits $520 into a savings account that has a 3.5% interest rate compounded monthly. How many years will it take to triple Jasmines investment?
About 31.4 years.