Algebra Homework

Prepared by Matthew S. Sutherland

Matching Models

Name Section Score /100 1.) For the following data table, y represents the height of a basketball when it is x feet away from the shooter. (25 pts. Each part is worth 5 points) x 0 2 4 6 10 12 14 16 18 20 y 6 15 22 27 31 30 27 22 15 6

a. Graph the data on the graph below

b. What is unique about the pattern this data makes compared to the other three?

c. Is the graph’s pattern linear, quadratic, rational, or exponential?

d. Choose the equation from the list at the end that best models this data

e. Use this equation to calculate the height of the basketball when it is 15 feet away.

Prepared by Matthew S. Sutherland

2.) For the following data table, y represents the total cost to make x number of sandwiches. (25 pts. Each part is worth 5 points) x 0 1 3 6 10 12 15 18 24 26 y 6 7.5 10.5 15 21 24 28.5 33 42 45

a. Graph the data on the graph below

b. What is unique about the pattern this data makes compared to the other three?

c. Is the graph’s pattern linear, quadratic, rational, or exponential?

d. Choose the equation from the list at the end that best models this data

e. Use this equation to predict the cost for making 40 sandwiches.

Prepared by Matthew S. Sutherland

3.) For the following data table, y represents the population (in thousands) of a town x years after 1990. (25 pts. Each part is worth 5 points) x 0 1 5 9 12 13 15 17 18 20 y 6 6.6 9.66 14.15 18.83 20.71 25.06 30.33 33.36 40.36

a. Graph the data on the graph below

b. What is unique about the pattern this data makes compared to the other three?

c. Is the graph’s pattern linear, quadratic, rational, or exponential?

d. Choose the equation from the list at the end that best models this data

e. Use this equation to predict the current population of this town.

Prepared by Matthew S. Sutherland

4.) For the following data table, y represents the number of fish (in hundreds) in a pond with limited resources x years after if was stocked. (25 pts. Each part is worth 5 points) x 0 2 4 8 10 12 16 20 26 28 y 6 14 18 22 23.14 24 25.2 26 26.8 27

a. Graph the data on the graph below

b. What is unique about the pattern this data makes compared to the other three?

c. Is the graph’s pattern linear, quadratic, rational, or exponential?

d. Choose the equation from the list at the end that best models this data

e. Use this equation to predict the number of fish in 100 years.

POSSIBLE EQUATIONS 𝑦 = 6(1.1)𝑥 𝑦 = 6(1.11)𝑥

𝑦 = 1

2 𝑥 + 6 𝑦 =

3

2 𝑥 + 6

𝑦 = − 1

4 𝑥2 + 5𝑥 + 6 𝑦 = −

1

4 𝑥2 + 6𝑥 + 6 𝑦 =

30𝑥 + 24

𝑥 + 4 𝑦 =

48𝑥 + 12

𝑥 + 2