Exponential Functions
Compound Interest
Graph Transformations
Logarithms
Applications
100
Is the function Exponential Growth or decay? Identify the y-intercept.
y=100(0.25)^x
Exponential Decay, 100
100
A principal of $2000 is placed in a savings account at 3% per year compounded annually. How much is in the account after one year, two years and three years?
1 year: $2060
2 years: $2121.80
3 years: $2185.45
100
Identify the parent function. Describe the transformations from the parent functions.
y=3x-2
y=3x
shift down 2
100
Write in logarithmic form 35 = 243
log3243 = 5
100
Suppose you deposit $600 into a savings account that pays 3.9% annual interest. How much will you have in the account after 3 years if no money as added or withdrawn?
$672.97
200
Is the function Exponential Growth or decay? Identify the y-intercept.
y=7/8(18)^x
Exponential Growth,
7/8
200
Find the amount compounded continuously.
Principal: $6000
Interest rate: 4.9%
Time: 10 years
$9793.90
200
Create a T chart to graph the following function
y=-(0.05)x+3
(-4,-20)
(-3,-1)
(-2,-0.05)
(-1,-0.025)
(0,-0.000125)
200
Evaluate without using a calculator
log864
2
200
The initial value of a car is $25,000. After 1 year, the value of the car is $21,250. Write an exponential function to model the expected value of the car. What is the cars value after 5 years?
y=25000(0.85)x
$11092.63
300
Graph the function. Find the Domain, Range,
and y-intercept.
y=-4(2)^x
(-2,-1),(-1,-2),(0,-4),(1,-8),(2,-16)
Domain: All Reals
Range: y<0
y-intercept: -4
300
Your 3 year investment of $20,000 received 5.2% interested compounded semi annually. What is your total return?
$23,329.97
300
Identify the parent function. Describe the transformations from the parent functions.
y=4log x+5
Parent function: y=log x
Stretch 4
Shift 5 up
300
Evaluate without using a calculator log1/5625
-4
300
A student claims the y-intercept of the graph of the function y=abx is the point (0,b). What is the students mistake? What is the actual y-intercept?
The y-intercept is when x=0. Plugging 0 into the function gives the point (0,a).
400
Evaluate to 4 decimal places using the table function in your calculator.
e5
148.4132
400
You invested $500 and received $650 after three years. What had been the interest rate? (Assume compounded continuously)
r = 0.087 or 8.7%
400
Graph y = log2x
400
Write in logarithmic form 8b = a
log8a = b
400
Nate opened a savings account and deposited $700.00 as principal. The account earns 11% interest, compounded continuously. What is the balance after 6 years?
$1354.35
500
Describe how y=5(2)x+1+3 compares to its parent function.
Stretch 5
left 1
up 3
500
Your 6 1/4 year investment of $40,000 at 14% compounded quarterly is worth how much now?
$94,529.80
500
For the function y=5x what will happen to the graph if we make x negative? (y=5-x)
It will reflect across the y-axis
500
Find the inverse of log4x = y
y = 4x
500
Compare the graph of y=log3(x+1) to the graph of its inverse y=3x-1. How are the graphs alike? How are they different?
Reflects across the line y=x
A domain shift in a logarithm is a range shift in the exponential
Exponential has a horizontal boundary line
Logarithm has a vertical boundary line