Graphing Exponential Functions
Does the function
f(x) = -2/9(5/4)x
represent exponential growth or decay?
Exponential growth
How is the function y = 2x transformed to create the graph of y = -2(x+3) - 4?
Translated left 3 units, reflected over the x-axis, and translated down 4 units.
Rewrite the equation in exponential form:
log464=3
43=64
Clue: The exponential form of the equation lnx=5
e5=x
Write a simplified exponential function for the scenario: an investment of $20,000 earns 2.5% interest per year.
y = 20000(1.025)x
Identify the y-intercept of the function:
f(x) = -6(1/4)x+3
(0, -0.09)
Write an example of a function that is translated right 3 units and up 5 units.
Answers vary.
Write the equation in logarithmic form:
2-3= 1/8
log2(1/8) = -3
What are the horizontal asymptote and the
The asymptote is y=-4
The y-intercept is approx. -1.28
A town starts with a population of 1,000 people, and it grows at a constant annual rate of 8%. This equation, f(t)=1000(1.08)t models the population over time in years. How much time has passed when the town has 1,469 people?
5 years
What is the end behavior of the graph of an exponential decay function?
As x approaches infinity, f(x) approaches the asymptote.
As x approaches negative infinity, f(x) approaches infinity.
Write an example of a function that shows a reflection in x and another example that shows a reflection in y.
Answers vary.
Evaluate using your knowledge of exponents (no calculators):
log255
1/2
A $1,000 investment in a Vanguard index fund grows at 8.1%. What is it's value in 5 years?
Approximately $1,500.
Tim's red F-150 was worth $20,000 when he bought it in 2022. It depreciates in value by 15% each year. How much is it worth this year?
$12,285.42
Graph y = 4(1/4)x
On paper.
Describe all the transformations applied to
f(x) = 4x to obtain the function f(x) = -2(4)x
How do these transformations affect the range of the function?
There are two transformations:
Effect on the Range: The original range was y> 0. The new range is y<0.
Write the expression that is equivalent to: log750 using the change of base formula and common logarithms. Do not evaluate.
log 50 / log 7
Students at B-P started coming down with a highly contagious virus. After t days, the number of people, P, who have been infected by the virus is modeled by the equation on your template. How many people have the virus after 7.95 years?
500 people
Carbon-14 has a half-life of 5,730 years. Brennan found an ancient bone that initially contained 100 milligrams of Carbon-14 and determined it was 11,460 years old. How many milligrams did it have when she found it? 25 milligrams.
25 milligrams
100(0.5)t/5730
Look at the base 2 graph. Write the equation of the function.
f(x) = (2)x+3 -5
What are two ways that a vertical stretch is different from a horizontal stretch?
For a vertical stretch, the number that is multiplied to the base is NOT in the exponent.
For a vertical stretch, the number that is multiplied in between 0 and 1 (a proper fraction).
Solve the equation for x: ln(x-4)=2
Show your work!
Approximately 11.389
Write the exponential function and fill in the blank.
x: 1, 2, 3, 4
y: 1536, 384, 96, ___
y=6144*0.25x, y = 24
A bank account earns 4% interest compounded continuously. If you invest $500, how long would it take to double your money?
17.3286 years
Use this equation: 1000=500e0.04t