Determine the initial value and the rate of change in the following description:

Question

Last year, Adrian's tomato plant reached a maximum height of 3 feet. He is growing another tomato plant this year, and he is tracking it's growth. The plant's height today is 12 inches, and it grows 1.5 inches each day.

A: initial value is b=1.5,rate of change is m=12
B: initial value is b=1.5, rate of change is m=3
C: initial value is b=3 rate of change is m=12
D: initial value is b=12 rate of change is m=1.5

Answer 1

To determine the initial value and the rate of change based on the description provided:

1. Initial Value (b): This refers to the starting height of the new tomato plant, which is given as 12 inches today.

2. Rate of Change (m): This is the amount by which the plant grows each day, which is stated to be 1.5 inches per day.

Given these interpretations:

• The initial value (b) is 12 inches (the height of the plant today).
• The rate of change (m) is 1.5 inches per day (the growth of the plant each day).

Now, let's analyze the options:

• A: initial value is b=1.5, rate of change is m=12 (Incorrect)
• B: initial value is b=1.5, rate of change is m=3 (Incorrect)
• C: initial value is b=3, rate of change is m=12 (Incorrect)
• D: initial value is b=12, rate of change is m=1.5 (Correct)

Thus, the correct answer is D: initial value is b=12, rate of change is m=1.5.