Exponent Rules
Properties of Exponential Functions
Growth or Decay?
Functions (from a table)
Functions (from a scenario)
Miscellaneous
100
Simplify: 4x (2x)0
4x
100
Consider the exponential function: f(x) = 3(12)x
What is the constant ratio?
b =12.
100
A function has a constant ratio(b-value) of 3.
Is this growth or decay?
growth - because 3 is greater than 1.
100
What's the y-intercept?
y-intercept: (0,5)
100
In 2010, your favorite snack cost $4. With inflation, the price is increasing by 1.5% each year.
Write a function to represent this scenario.
f(x) = 4(1+0.015)x or f(x) = 4(1.015)x
100
A function is increasing by 45%. What is the constant ratio (b-value)?
b = 1 + 0.45
b = 1.45
200
Simplify: 3x(2x4)
6x5
200
Consider the exponential function: f(x) = 10(0.5)x
What is the y-intercept?
The y-intercept is (0, 10)
200
A function has a constant ratio(b-value) of 0.3.
Is this growth or decay?
Decay - because 0.3 is less than 1.
200
What's the constant ratio?
b =2
200
Write an exponential function for this scenario.
f(x) = 12,000(1+0.06)x
or f(x) = 12,000(1.06)x
200
A function is decreasing by 20%. What is the constant ratio (b-value)?
b = 1 - 0.2
b = 0.8
300
Simplify: (a3b12)/(a2b7)
ab5
300
What is the difference between a linear function and an exponential function?
Linear functions have constant change (adding the same amount).
Exponential functions don't have constant change, but they do have a constant ratio (multiplier).
300
f(x)=25(1.07)x
Does this function represent exponential growth or decay?
Exponential Growth.
300
Write the exponential function represented by this table. (Round the constant ratio)
f(x) = 5,005(1.2)x
300
Write the function AND answer the question.
Function: f(x) = 18,000(1 - 0.02)x
or f(x) = 18,000(0.98)x
After 3 years the population will be: 16,941 people
300
A function is increasing by 2%. What is the constant ratio (b-value)?
b = 1 + 0.02
b = 1.02
400
Simplify: 2x-4
2/x4
400
In order to be an exponential function, the constant ratio (b-value) cannot be ___________________?
The constant ratio cannot be a negative number.
400
f(x)=1300(0.98)x
Does this function represent exponential growth or decay?
Exponential Decay
400
Write the exponential function represented by this table.
f(x) = 2100(1.03)x
400
You put $500.00 into an account and the account earns 4% interest, compounded annually (each year). How much will be in the account after 5 years?
Write the function AND answer the question.
Function: f(x) = 500(1 + 0.04)x
or f(x) = 500(1.04)x
After 5 years, the account will have: $608.33
400
A zombie outbreak is modeled by the function where x measures the number of days:
f(x) = 4(1.15)x.
1) How many zombies started the outbreak?
2) How many zombies will there after a week (7 days)?
1) 4 zombies started the outbreak
2) There will be 10 zombies after 7 days.
500
Simplify: (3m2)3
27m5
500
What is the name of the horizontal line that an exponential function will get closer and closer to, but never touch?
a horizontal asymptote
500
f(x)=25(1)x
Does this function represent exponential growth or decay?
Neither!
500
Write the exponential function represented by this table.
f(x) = 20(0.5)x
500
Your car cost $42,500 when you purchased it in 2015. The value of the car decreases by 15% annually (each year)
What is the value of your car now?
f(x) = 42,500(1 - 0.15)x or
f(x) = 42,500(0.85)x
Your car's value now (8 years later) is: $11,580.85
500
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