Question

Cecelia planted two bushes at the same time and measured their heights over several years. She represented each bush's growth as shown.

Bush A:
Had a height of 7.5 in. when planted;
Grew at a constant rate of 2.5 in. per year
Bush B:
Bush Height (in.)
36
32
28
24
20
16
12
1 2 3 4 5 6 7 8 9 10
Years Since Planted

1. Which bush has the greater initial value?

A) Bush A
B) Bush B
2. Which bush has a greater rate of change?

A) Bush A
B) Bush B
3. After 7 years what will be the height of each bush be?

Answer 1

Bush B has the greater initial value and rate of change. After 7 years, Bush A will be 25 inches tall and Bush B will be 78 inches tall.

Step-by-step explanation:

1. The initial value of Bush A is 7.5 inches, while the initial value of Bush B is 36 inches. Therefore, Bush B has the greater initial value.

2. The rate of change for Bush A is 2.5 inches per year, while the rate of change for Bush B is 6 inches per year. Therefore, Bush B has the greater rate of change.

3. After 7 years, the height of Bush A will be 7.5 + (2.5 * 7) = 7.5 + 17.5 = 25 inches. The height of Bush B will be 36 + (6 * 7) = 36 + 42 = 78 inches.