Which of the following situations describes exponential growth?

A car's value decreases by 1,000 dollars each year.

A runner's speed increases by 0.1 m/s every minute.

A social media post's shares triple every hour.

A swimming pool is filled at a rate of 20 gallons per minute.

Consider the function in the table. What type of function is it? | $x$ | $f(x)$ | |:---:|:------:| | 0 | 5 | | 1 | 15 | | 2 | 45 | | 3 | 135 |

Linear, because the values increase by 10.

Exponential, because each $f(x)$ value is the previous one multiplied by 3.

Linear, because the x-values increase by 1.

Exponential, because the values are increasing.

Graphing and Comparing Linear, Quadratic, and Exponential Functions Practice — Grade 9 math

Lesson 119: Graphing and Comparing Linear, Quadratic, and Exponential Functions — Practice Questions

1. A colony of bacteria starts with 50 cells and doubles in size every hour. How many cells will be in the colony after 4 hours? ___ cells.
2. Which of the following situations describes exponential growth?
- A. A car's value decreases by 1,000 dollars each year.
- B. A runner's speed increases by 0.1 m/s every minute.
- C. A social media post's shares triple every hour.
- D. A swimming pool is filled at a rate of 20 gallons per minute.
3. The value of a collectible action figure is modeled by the function $V(t) = 60 \cdot 2^t$, where $t$ is the number of years. What was the initial value of the action figure? ___ dollars.
4. Consider the function in the table. What type of function is it? | $x$ | $f(x)$ | |:---:|:------:| | 0 | 5 | | 1 | 15 | | 2 | 45 | | 3 | 135 |
- A. Linear, because the values increase by 10.
- B. Exponential, because each $f(x)$ value is the previous one multiplied by 3.
- C. Linear, because the x-values increase by 1.
- D. Exponential, because the values are increasing.
5. A scientist observes a sample of 20 mold spores. The number of spores quadruples every day. How many spores will there be after 3 days? ___ spores.
6. A population of rabbits in a park doubles every year. Which type of function best models the rabbit population over time?
- A. Linear
- B. Quadratic
- C. Exponential
- D. Constant
7. A diver jumps from a platform. The path of the diver's height goes up initially and then back down to the water. Which function family best describes this path?
- A. Linear
- B. Quadratic
- C. Exponential
- D. None of the above
8. Leo earns money by mowing lawns. He charges a flat fee of $30 for each lawn he mows. The function relating his total earnings to the number of lawns mowed is ___. (linear/quadratic/exponential)
9. A function whose graph is a non-vertical straight line and shows a constant rate of change belongs to the ___ function family.
10. A scientist observes a culture of 100 cells. The number of cells increases by 25 cells every hour. Which function family models this situation?
- A. Linear
- B. Quadratic
- C. Exponential
- D. Cannot be determined