Graphing Exponential Functions
Using Exponent Properties
Evaluating Exponential Functions
Writing Exponential Functions
Exponential Growth & Decay
100
True or false: An exponential function has a graph that shows a constant rate of change
False
100
What is 2000?
Explain how you know...
1
ANYTHING to the Zero power is always 1
100
Evaluate y = 32(1.21)x when x = 5, rounded to the nearest 10th
83
100
Write the exponential function:
y-intercept = 0.2
constant multiplier = 5
y = 0.2(5x)
100
Does this function represent exponential growth or decay? How can you tell?
y = 135 (1 - 0.05)x
decay, the factor of increase is less than one
200
Fill in the blanks: When graphing an exponential function in the form y=abx, the letter _____ represents the y-intercept and the graph will open ____ if ____ > 0
a , up , a
200
Simplify this using exponent properties:
43 * 42 =
What did you do to the exponents?
45
Add them - this is the Product of Powers property
When multiplying exponential expressions with the same base, simply add up the exponents
200
Evaluate the function f(x)= 1.5(4-x)
when x = 2
0.09375
200
An exponential function starts at 3 and triples every time x goes up by 1.
Write a function that represents this situation.
f(x) = 3(3x)
200
Is this function growth or decay? How can you tell?
y = 40 (4x)
growth, the factor of increase is greater than one
300
Make the table of 5 values you would use to graph this function:
f(x) = 3(3)x
x: -2, -1, 0, 1, 2, 3, 4
y: 1/3, 1, 3, 9, 27, 81, 243
300
Simplify using exponent properties:
56/54 =
52
56/54 = 56-4 = 52
Quotient of Powers Property - When dividing exponents with the same base, simply subtract the bottom from the top
300
You buy a car for $27,000. The following equation represents the depreciation of a car over x years. Find the value of the car 5 years from now.
V(x) = 27,000(0.96x)
$22,015.06
300
A $14,000 truck is worth $12,320 the next year. Write the exponential function for this scenario if the value continues to decrease at the same rate each year.
y = 14000 * 0.88x
300
Kayden's antique car is worth $12,000. It appreciates in value by 11% each year. Write the exponential function for this scenario.
y = 12000 (1 + .11)x or y = 1200*1.11x
400
Graph y = 4(1/4)x
x: -2, -1, 0, 1, 2
y: 64, 16, 4, 1, 1/4
400
Simplify using exponent properties:
(32)4 =
38
(32)4 = 32*4
Power of a Power Property: When taking an exponent to another power, simply multiply the exponents
400
A $300,000 house appreciates in value by 11% each year. How much will the house be worth in 3 years?
V(x)= 300,000(1.11x)
$410,289.30
400
Write the exponential function and fill in the blank.
x: 1, 2, 3, 4
y: 1536, 384, 96, ___
y=6144*0.25x, y = 24
400
Harold's credit card has 14% annual interest. His starting balance is $3000. How much will he owe in 3 years if he makes no other payments or charges to the card? (Harold is making a very bad financial choice)
What is $4,444.63
500
y = 8 (1/2)x
500
Simplify using exponent properties so the answer only has positive exponents:
6-2 =
1/62
Negative Exponent property example:
x-2= 1/x2
To rewrite negative exponents, turn the expression into a fraction with 1 over the same thing with a positive exponent
500
Fill in the blank for this exponential function.
x: -2, -1, 0, 1, 2
y: 0.625, 0.25, ??, 4, ??, 64
1, 16
500
A bank is offering a savings account with a growth rate of 1.02. Write the exponential function for this scenario if you initially deposit $650.
y = 65 (1.02x)
500
Find the percent of change, growth or decay, and fill in the bank:
x: 0, 1, 2, 3
y: 800, 600, 450, ___
25% decay, 337.5