Writing Equations
Linear vs. Exponential
Exponential Increase vs. Decrease
Power to a Power
Different Compounding Intervals
TRIVIA
100
The enrollment of a school is growing by 2% per year. The school currently has 1,250 students. Write an equation to represent the enrollment in 4 years if this growth continues.
y=1,250*(1.02)^4
100
Is the following relationship Linear or Exponential?
Linear
(adding 35 each time x increases by 1)
100
Does the following equation represent an exponential increase or decrease?
y=35 * (.97)^x
Decrease
A decrease of 3%
100
3^10
100
A savings account earns 6% annual interest. If this interest is calculated semi-annually for 5 years what number goes in the equation?
1000 ((???)^2)^5
1.03
6% annual interest calculated twice a year is 3% two times for 5 years.
100
What year was Everett High School founded
1880
200
Which of the variables represents the initial value in an exponential equation?
y=a*b^x
a
200
If this table represents an EXPONENTIAL relationship, what is the next number in the table
140
(y is multiplied by 2 each time x increases by 1)
200
The following equation shows an exponential increase of a population. What is the growth rate (by what percent is it changing)?
250 * (1.025)^x
2.5%
200
1
200
Which equation shows a $500 balance on a credit card with 20% annual interest compounded quarterly for 2 years?
500((1.20)^4)^2
500(1.05)^2
500((1.05)^4)^2
500((1.05)^4)^2
200
How are Phineas and Ferb related?
They are step brothers
300
In 1990 my Air Jordans were valued at $125. I have been told that they have increased in value by 3% each year.
Write an exponential equation to show what they were worth in 2020.
125*(1.03)^30
300
Write an equation to model the following relationship
y=100 * (1.10)^x
300
SELECT ALL equations that represent a 12% decrease
400*(1.12)^x
400*(1-0.12)^x
400*(.88)^x
400*(.12)^x
400*(1-0.12)^x
400*(.88)^x
300
Write as a power to a power
A bug population is growing 4% per month for two years
((1.04)^12)^2
300
Calculate the total balance on a $2000 loan with 30% annual interest applied monthly for 2 years.
$ 3617.45
2000((1.025)^12)^2)
300
How many days until Spring Break?
2 Full Days (not counting today)
3 Days (counting today)
400
Movie attendance at theatres began decreasing by 7% each year starting in 2009. If 1.4 billion people went to the movies in 2009, write an equation representing how many people went in 2014
1.4 *(1-.07)^5
1.4*(.93)^5
400
Both equations below show accounts that are earning interest. How many years do you have to wait until Option 2 has more money?
Option 1: 100 + 25x
Option 2: 100 * (1.15)^x
At year 8 Option 2 will have more money
100 + 25 (8) =300
100 * (1.15)^8 = 305.90
400
A car's value decreases by 15% each year.
If you purchase a 20,000 car, what is it worth in 5 years? (round to the nearest dollar)
$8,874
20,000 *(1-0.15)^5
400
Which of the following does NOT represent a 15% yearly increase to an initial baseball card collection of 200 cards for 2 decades
200 * ((1 + .15)^10)^2
200+(1.15)*20
200 *(1.15)^20
200 + (1.15)*20
400
You have a $10,000 loan with 22% annual interest.
After one year, how much more interest would you end up owing if they calculated the annual interest quarterly (HINT: 5.5% 4 times a year)
$188
Amount owed if they applied annual interest once a year 10,000(1.22)^1=12,200
Amount owed if they applied annual interest quarterly
10,000((1.055)^4)^1=12,388
400
What does "lamination" refer to in baking?
Lamination is the process of folding and rolling butter into dough over and over again to create super-thin layers.
