choosing the model that fits the data: linear, quadratic or exponential

Grade 11 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

1.
0 → 15; 1 → 22; 3 → 36; 5 → 50. The weeks are not evenly spaced. Milo records the dollars in a class savings jar on weeks 0, 1, 3 and 5. Which model fits, and what does it do each week?
- Exponential: the jumps grow from $7 to $14 as the weeks go on
- Quadratic: the jumps $7, $14 and $14 keep changing
- Linear: it adds $7 every week
2.
0 → 400; 1 → 320; 3 → 204.8; 5 → 131.1. Noah tracks a used scooter's value in dollars at years 0, 1, 3 and 5. Which model fits, and what does it do every year?
- Exponential: the value is multiplied by 0.8 every year
- Linear: the value drops by 80 every year, so it hits 0 in year 5
- Quadratic: the drops 80, 115.2 and 73.7 keep changing
3.
1 → 5; 2 → 10; 3 → 19; 4 → 32; 5 → 49. Pia's patio pattern has 5, 10, 19, 32 and 49 tiles in steps 1 to 5. Which equation fits every step?
- y = 4x² − 7x + 8
- y = 2x² − x + 4
- y = 5(2)^(x − 1)
- y = 2x² + 3
4.
0 → 80; 5 → 40; 10 → 20; 15 → 10. Esme measures the grams of dye left in a tank at minutes 0, 5, 10 and 15. Which equation fits every row?
- y = 80(1/2)^x
- y = 80(1/2)^(x/5)
- y = 80 − 8x
5.
0 → 6; 1 → 54; 2 → 70; 3 → 54; 4 → 6. Zee records a thrown ball's height in feet each second from 0 to 4. Which equation fits every row?
- y = 16x² − 64x + 6
- y = −16x² + 64x + 6
- y = 6 + 48x
- y = −32x² + 80x + 6
A model for the grams of dye in a tank is P = 800(0.5)^(t/6), with t in days. To the nearest tenth, what percent change per day does Bo read? A decrease is negative.
A model for a used car's value in dollars is V = 1,500(0.8)^(t/3), with t in years. To the nearest tenth, what percent change per year does Jun read? A decrease is negative.
Technology fits y = 250(1.06)^x to a town's daily bike-share rides after x years. After how many years does Kira's model reach 400 rides, to the nearest tenth?
Technology fits y = 80(1.5)^x to the leaves in a duckweed patch after x days. After how many days does Luz's model reach 500 leaves, to the nearest tenth?
Technology fits y = 1,500(0.9)^x to a used car's value in dollars after x years. After how many years does Milo's model fall to $800, to the nearest tenth?

choosing the model that fits the data: linear, quadratic or exponential

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1.
0 → 15; 1 → 22; 3 → 36; 5 → 50. The weeks are not evenly spaced. Milo records the dollars in a class savings jar on weeks 0, 1, 3 and 5. Which model fits, and what does it do each week?
- Exponential: the jumps grow from $7 to $14 as the weeks go on
- Quadratic: the jumps $7, $14 and $14 keep changing
- Linear: it adds $7 every week
2.
0 → 400; 1 → 320; 3 → 204.8; 5 → 131.1. Noah tracks a used scooter's value in dollars at years 0, 1, 3 and 5. Which model fits, and what does it do every year?
- Exponential: the value is multiplied by 0.8 every year
- Linear: the value drops by 80 every year, so it hits 0 in year 5
- Quadratic: the drops 80, 115.2 and 73.7 keep changing
3.
1 → 5; 2 → 10; 3 → 19; 4 → 32; 5 → 49. Pia's patio pattern has 5, 10, 19, 32 and 49 tiles in steps 1 to 5. Which equation fits every step?
- y = 4x² − 7x + 8
- y = 2x² − x + 4
- y = 5(2)^(x − 1)
- y = 2x² + 3
4.
0 → 80; 5 → 40; 10 → 20; 15 → 10. Esme measures the grams of dye left in a tank at minutes 0, 5, 10 and 15. Which equation fits every row?
- y = 80(1/2)^x
- y = 80(1/2)^(x/5)
- y = 80 − 8x
5.
0 → 6; 1 → 54; 2 → 70; 3 → 54; 4 → 6. Zee records a thrown ball's height in feet each second from 0 to 4. Which equation fits every row?
- y = 16x² − 64x + 6
- y = −16x² + 64x + 6
- y = 6 + 48x
- y = −32x² + 80x + 6
A model for the grams of dye in a tank is P = 800(0.5)^(t/6), with t in days. To the nearest tenth, what percent change per day does Bo read? A decrease is negative.
-10.9
A model for a used car's value in dollars is V = 1,500(0.8)^(t/3), with t in years. To the nearest tenth, what percent change per year does Jun read? A decrease is negative.
-7.2
Technology fits y = 250(1.06)^x to a town's daily bike-share rides after x years. After how many years does Kira's model reach 400 rides, to the nearest tenth?
8.1
Technology fits y = 80(1.5)^x to the leaves in a duckweed patch after x days. After how many days does Luz's model reach 500 leaves, to the nearest tenth?
4.5
Technology fits y = 1,500(0.9)^x to a used car's value in dollars after x years. After how many years does Milo's model fall to $800, to the nearest tenth?
6