Modeling Exponential Functions
Linear or Exponential? What Gives It Away?
Properties of Exponents
Marvel
Cereal Mascots
100
In the equation y=ab^x , what does the b stand for?
The growth/decay factor
100
A worker earns $15 per hour. Is this situation linear or exponential?
Linear (adds $15 every hour)
100
Simplify
(x^3)(x^5)
x^8
100
What is the real name of Iron Man?
Tony Stark
100
Tony the Tiger
Frosted Flakes
200
In the exponential function y=5(2)^x , what does the number 5 represent?
The initial amount
200
A population of bacteria starts at 500 and triples every hour. Is this situation linear or exponential?
Exponential (triples)
200
Simplify
(x^4)^6
x^24
200
What superhero's real name is Bruce Banner
The Hulk
200
A Silly Rabbit
Trix
300
A car’s value depreciates by 15% each year. If the car was originally worth $20,000, write an equation modeling its value after x years.
y=20000(1-0.15)^x
, or
y=20000(0.85)^x
300
A car’s value decreases by $2,000 per year. Is this situation linear or exponential?
Linear (decrease at a constant rate of 2000 every year)
300
3x^5*4x^-5
12
300
What is the name of the secret African country ruled by Black Panther?
Wakanda
300
A bee
Honey Nut Cheerios
400
If a population of bacteria doubles every hour and starts with 100 bacteria, what is the equation modeling the population after x hours?
y=100(2)^x
,or
y=100(1+1)^x
400
A store discounts an item by 10% each time it goes unsold for a week. Is this situation linear or exponential?
Exponential (the % gives it away)
400
Simplify
(3x^2)/x^3
3/x
400
What is Captain America's shield made of?
Vibranium
400
Crazy Squares
Cinamon Toast Crunch
1000
An investment grows according to the formula A=P(1+-r)^t . If $1,000 is invested at an annual interest rate of 5%, how much will it be worth after 10 years?
$1,628.89
1000
A radioactive substance loses half of its mass every 10 years. Is this situation linear or exponential?
Exponential (half mean multiply by 1/2)
1000
(16x^4y^4z^4)/(2x^6y^3z^4)
(8y)/x^2
1000
What superhero did actors Tobey Maguire, Andrew Garfield, and Tom Holland all play?
Spiderman
1000
Cinna-Mon
Apple Jacks