Choosing the Best Function for a Math Model (Grade 10)

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Choosing the Best Function for a Math Model

1. 
A bird dives off of a branch toward the water. After 1 second it has traveled 1 meter, after 2 seconds it has traveled 2 meters, and after 3 seconds it has traveled 4 meters. The function which best describes the distance traveled over time is
  1. linear.
  2. exponential.
  3. logarithmic.
  4. none of the above.
2. 
Jose is making a soup mix that says 1 cup of mix for 3 servings, 2 cups for 6 servings, or 3 cups for 9 servings. The function which describes the ratio of mix to servings is
  1. linear.
  2. exponential.
  3. logarithmic.
  4. none of the above.
3. 
A car's value depreciates each year by about 15%. Which function would best model the car's value depending on the number of years the owner has had it?
  1. Linear
  2. Exponential
  3. Quadratic
  4. None of the above
4. 
Tom's savings account earns 0.5% simple interest each year. Which type of function would best model the growth of the money in Tom's account over time?
  1. Linear
  2. Exponential
  3. Quadratic
  4. Cubic
5. 
A certain plant will triple the amount of area it covers in a garden each year. Which type of function would best describe the yearly growth of this plant?
  1. Linear
  2. Exponential
  3. Quadratic
  4. None of the above
6. 
It is raining where Sarah lives, and she is watching a cup that is outside fill with water. Every ten minutes, the water level is 1 cm higher. Which type of function would best describe the increasing water level over time?
  1. Linear
  2. Exponential
  3. Square root
  4. None of the above
7. 
Evan is hiking down a mountain on a trail that is 12 miles long. He notices that every 30 minutes, he has hiked about 5% of the total distance from the top of the mountain to his camp site. Which type of function would best describe the distance he has hiked, given the amount of time that has elapsed since he started down the mountain?
  1. Linear
  2. Exponential
  3. Logarithmic
  4. None of the above
8. 
A certain substance has been created that dissolves very slowly in water. Every hour, half of the remaining substance dissolves. Which type of function would best model how much of the substance is left after a given number of hours?
  1. Linear
  2. Exponential
  3. Cubic
  4. None of the above
9. 
Christina is on a Ferris wheel, and she will stay on for several rotations. As she goes around, her vertical height from the ground can be measured. Which of the following types of functions would best model her vertical height given the amount of time that has passed since she first got on?
  1. Linear
  2. Exponential
  3. Quadratic
  4. None of the above
10. 
Pedro is making a loaf of sourdough bread. He is at the stage of preparing the dough where he needs to let it sit out on the counter, covered, while it rises. At the current room temperature where the dough is sitting, it will increase in volume by about 15% every hour. Which type of function would best model the growth in volume of the dough over time?
  1. Linear
  2. Exponential
  3. Quadratic
  4. None of the above

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