Which Family
A company is selling computer programs. The first program costs $80, and each additional program costs $60.
Linear
For every 15 minutes spent studying, you are projected to earn 6 points on an upcoming test. If you spend 2 hours studying, what is your projected score? (The test has 50 points possible.)
48/50
A colony of bacteria currently has 50 bacteria in it. If it quadruples every day, how many bacteria will there be 6 days from now?
204,800 bacteria
The concentration of a certain medication left in the body after x hours is given by the equation below. What is the concentration left in the body after 7 hours?
C(x) = 50/x + 8
15.14
A startup company is doubling its sales of a new product every 3 months. If it made 2000 sales when it launched the product, how many sales will it be making in its 18th month?
128,000
A soccer ball is kicked to a player across the field.
Quadratic
When you purchase an item online, there is a flat rate shipping fee of $2.95, plus $0.35 per pound of the item shipped. How much is the shipping fee for an item that weighs 8 pounds?
$5.75
The half-life a certain radioactive element is 5 hours. If you start with 50 radioactive atoms of the element, how many atoms will still be radioactive after 8 hours?
16 radioactive atoms
The altitude y (in feet) of a plane t minutes after takeoff is approximated using the function below. How high will the plane be after 90 minutes?
y(t) = 5000 log(0.05t) + 8000
about 11,266 feet
A water treatment facility has a cylindrical storage tank. When they open the drain valve, the volume of water remaining in the tank (in gallons) after t minutes is modeled by the equation below. How much water is left after 5 minutes?
V(t) = -0.5t3 + 12t2 - 60t + 1000
937.5 gallons
The population of Whiteland increases by 3% each year.
Exponential
Students are observing the growth of a plant in their 6th grade science class. It was 2" tall when they planted it, and it grows 3" per week. How tall will it be after 19 weeks?
59"
The population of Medway, Ohio was 4007 in 2000. It decreased by about 0.36% per year until 2020. What was the population in 2020?
3728 people
The value of a truck depreciates by 15% each year it is driven. If a a landscaping company purchased a truck for $40,000 in 2018, how much will that same truck be worth in 2028?
about $7875
Alani has a summer job as a lifeguard. She earns a base pay of $50 and then earns an additional $10 for each hour she works. If she worked 32 hours this week, how much money did she make?
$370
The half-life of a certain radioactive isotope is 8 days.
Exponential
Your cell phone company charges $100 per month for a basic phone plan. They also charge $4.15 for each GB of data used. You used 3.6 GB of data this month. How much will your bill be?
$114.94
You start with $60 in your savings account, and earn 15% interest each year. How many years will it take to have $600 if you don't add any more money to the account yourself?
16.5 years
You use a trebuchet to launch a water balloon. It's height in feet each second after launch is modeled by the equation below. What time will the balloon hit the ground?
h(t) = -16t2 + 64t + 5
4.08 seconds after launch
The height of a tree (after t years) is given by the equation below. If the tree is planted today, how many years will it be until the tree is 46 feet tall?
h(t) = 40 log(t) + 3
11.9 years
A company is selling books. For every decrease of $1 in the price, they sell 12 more books. For every increase of $1 in the price, they sell 8 fewer books.
Quadratic
Jasmine is treating her friends to a movie. They shared a large popcorn that cost $6.50. They all got drinks that cost $4.50 each. If her total was $24.50, how many people went to the movies?
4 people (including Jasmine)
The temperature of a pizza that just came out of the oven is 425°. The pizza should not be eaten until it cools down to 100°. If its temperature drops by 30% each minute, how long will it be until you can eat it?
4 minutes
The profit made by a sweatshirt sale is modeled by the equation below. At what price should you sell the sweatshirts in order to maximize your profit?
P(x) = -0.02x4 + 2.24x3 - 94.08x2 + 1756.16x - 12253.12
$28
You design a rectangular garden, and have 60 feet of fence available and want to maximize the area. If x is the width of the garden, what is the greatest area you can have?
A(x) = -2x2 + 60x
about 449 square feet