Exponential Functions
Fill in the blanks: Exponential Functions are modeled using f(x) = a ∙ bx, where a is the ________ and b is the __________.
initial amount/y-intercept, growth/decay factor
Simplify:
m6x-5y8
________
m5x2y-4
my12
_______
x7
Given the exponential function formula below:
f(x) = a(b)x + k
What does k represent?
A vertical translation/shift
What is the formula we use for exponential growth functions?
f(t) = a(1 + r)t
What is the formula we use to calculate compound interest?
A = P(1 + r/n)n*t
In the exponential function below:
f(x) = 2(3)x, what is the initial amount/y-intercept?
a = 2
Convert 260,000,000 to scientific notation.
2.6 * 108
Given the exponential function formula below:
f(x) = a(b)x-h
What does h represent?
A horizontal translation/shift
In the exponential formula,
f(t) = a(1 ± r)t, "1±r" is known as the _______.
growth/decay factor
In the formula, A = P(1 + r/n)n*t, what does n represent?
n = number of periods/times compounded each year
In the exponential function below:
f(x) = 4(1/2)x, what is the decay factor?
b = 1/2
Convert 5.7 * 10-5 to standard form.
Given the exponential function formula below:
f(x) = a(b)x
What happens to graph if a is > 1?
The graph stretches.
A video is labeled a fan favorite if it receives at least 1,000 views per day. Amelia posts a video that gets 6,465 views on the first day. The number of views decreases by 20% each day after that. In how many days total will the video stop being a fan favorite?
9 days
What would be substituted for n in the compound interest formula if interest is compounded semi-annually?
2
What is the written form of the exponential function represented by the given table:
x y
0 4
1 12
2 36
3 108
f(x) = 4(3)x
Solve: *NO CALCULATOR*
(9 x 104) x (2 x 109)
1.8 * 1014
f(x) = (0.5)x + 3
Describe the transformation.
Vertical translation 3 units up.
The population of Hillville is 10,000 residents and grows at an annual rate of 20%. What will the estimated population of Hillville be in five years?
24,883 residents
Rosa's family invested in a Certificate of Deposit (CD) for $5,000 when she was born. The interest earned is 6% and is compounded quarterly. What is the value of the CD after 18 years?
$14,605.79
In the exponential function below, what is the growth rate?
f(x) = 2(3)x
200%
Solve: *NO CALCULATOR*
1.28 x 109
__________
2 x 106
6.4 * 102
Describe the transformation given the function below:
f(x) = 3(4)x-2 - 3
Horizontal translation 2 units to the right. Vertical translation 3 units down. Y-intercept = 3, which shows a stretch
The value of a pair of Fire Red 4 Jordan's increases by 10 percent every year. If the shoes were purchased 9 years ago for $140, how much is it worth today?
Approximately $330
Tyler is saving up for a new car and puts $7,500 into an account that offers 7% interest compounded quarterly. What will be the amount of the interest after 8 years? DO NOT ROUND UNTIL FINAL ANSWER
$5,566.60