Question

A zucchini plant in Darnell’s garden was 13 centimeters tall when it was first planted. Since then, it has grown approximately 0.6 centimeter per day.
a. Write a rule to describe the function.
b. After how many days will the zucchini plant be 0.208 meter tall?





h(d) = 13d + 0.6; 1.6 days


h(d) = 0.6d + 13; 13 days


h(d) = 0.6d; 35 days

Answer 1

To model the growth of the zucchini plant over time, we can establish a function based on the information provided.

### a. Write a rule to describe the function.

Let \( h(d) \) represent the height of the zucchini plant in centimeters after \( d \) days. The plant starts at 13 centimeters and grows at a rate of 0.6 centimeters per day. Therefore, the function can be written as:

\[
h(d) = 0.6d + 13
\]

### b. After how many days will the zucchini plant be 0.208 meter tall?

First, we need to convert 0.208 meters to centimeters, since our function is in centimeters. Since 1 meter equals 100 centimeters:

\[
0.208 \text{ meters} = 0.208 \times 100 = 20.8 \text{ centimeters}
\]

Now, we set the function equal to 20.8 centimeters and solve for \( d \):

\[
0.6d + 13 = 20.8
\]

To isolate \( d \), first subtract 13 from both sides of the equation:

\[
0.6d = 20.8 - 13
\]
\[
0.6d = 7.8
\]

Now, divide both sides by 0.6:

\[
d = \frac{7.8}{0.6} = 13
\]

Thus, the zucchini plant will reach a height of 0.208 meters (20.8 centimeters) after **13 days**.

### Summary:
- The rule is \( h(d) = 0.6d + 13 \).
- The plant will be 0.208 meters tall after **13 days**.

Therefore, the correct answer for both parts would be:

**h(d) = 0.6d + 13; 13 days.**