Exponential Functions
What kind of exponential function does the equation represent below? (growth, decay, neither)
(1/2)^x
decay
Landon and Judah decided to play Fortnite after completing their 7.1.4 Review + Preview homework together. Thanks to Judah, their opponents were dropping like flies. The equation that represented this is y=100(9/10)^x where x represents minutes that passed by. How many opponents were left after 2 minutes passed?
81
(plot twist: Landon carried Judah)
Aly, Elliott, and Carson were being clumsy and accidentally dropped a bouncy ball from the top of a sky scraper at 140 meters. It bounced back up to 112 meters after the first bounce. It then bounced back up to 89.6 meters after the second bounce. Write an equation to represent their scenario.
y=140(.8)^x
Write this in a different form:
(1/5)^-1
5
Multiply this out:
(x+6)^2
x^2 + 12x + 36
What kind of exponential function does the equation represent below? (growth, decay, neither)
6^x
growth
Colin was on a rampage to see how many pictures he could put up of Matt in one day around the school. He was preparing this project at home. He started with 4 copies of Matt's face and grew his pile, multiplying the pictures by x3 per minute.
Write an equation representing this.
4(3)^x
Alice's company is growing very quickly. Her number of employees, y, can be found using the equation, where x represents the number of years.
y=16(3)^x
State what each number means in this scenario
16= how many employees started in Alice's company
3=multiplier (growing x3 per year)
Write this in a different form:
2^-5
1/32
The correlation coefficient in regard to doing your homework and getting good grades is r=.99
What does this mean in context?
If you do your homework, you'll get better grades
What kind of exponential function does the equation represent below? (growth, decay, neither)
1^x
Neither. The function is a linear, horizontal line
Lucia and Kinsley wanted to get that bread so they put money in a savings account. Kinsley chose to do simple interest and Lucia chose Compound interest. Which is better after 3 years? 10 years?
y=90x+1000 (simple interest)
y= 1000(1.08)^x (compound interest)
simple after 3
compound after 10
Both Eliza and Izzy's dream jobs are to become teachers alongside Mr. Hardin and Mrs. Radcliffe (so sweet). They will start at a $40,000 salary and it will increase by 3% each year. Write an equation for their salary
40,000(1.03)^x
Write this in a different form:
(1/3)^-2
9
f(n)= 7n + 96
What is the value of n when f(n) = 145
7
What kind of exponential function does the equation represent below? (growth, decay, neither)
0^x
neither, linear horizontal line through y=0
Grace and Ace were studying the carbon-14 decay in dinosaur fossils. If the dinosaur contained 200 grams of carbon 14 originally, how much will it contain after 4 half lives?
12.5 grams of carbon
Logan wanted to continue his gambling addiction at the casino. He walked in with $10,000 and gained about $200 per hour. Write an equation representing Logan's money over time
y= 10,000 + 200x
Write this in a different form:
(3/2)^-1
2/3
The amount of money Mr. Krabs makes by selling Krabby Patties can be expressed by the equation y= 4x -32 where y= money and x=burgers sold
Does the y intercept make sense in context?
What kind of exponential function does the equation represent below? (growth, decay, neither)
y= (3.14159265358979323846)^x
growth
Riley and Jane LOVE Taylor swift. Elon musk generated a teleportation device that brings Taylor swift closer to Riley and Jane every day. How far will Taylor be after a year?
y = miles x = days passed
y= 20,000(.98)^x
12.5 miles away
Rylan and Keaton started working out at their local gym. Their bench press was exponentially growing the more they worked out each month (represented by x). Label what each part of the equation represents.
y= 85(1.2)^x
They started at 85 pounds
Multiplied by 1.2 each month
Write this in a different form:
(2/3)^-3
27/8
What is Mr. Hardin's first name?
Joey