Question

Some students can plant 9 carrots per square foot in the community garden shown. Write a function f that can be used to determine the number of carrots the students can plant. Give a reasonable domain for the function. How many carrots can the students plant in a garden that is square with​ 4-ft side​ lengths?

Answer 1

To determine the number of carrots that students can plant in a community garden, we can define a function \( f \) that relates the area of the garden to the number of carrots planted.

Let:
- \( s \) represent the side length of the square garden in feet.
- The area \( A \) can be calculated using the formula for the area of a square, \( A = s^2 \).
- Since the students can plant 9 carrots per square foot, the number of carrots \( f(s) \) they can plant is given by:

\[
f(s) = 9 \cdot A = 9 \cdot s^2
\]

So the function can be stated as:

\[
f(s) = 9s^2
\]

### Reasonable Domain
A reasonable domain for the function consists of non-negative values of \( s \) because the side length cannot be negative. Therefore, the domain of the function is:

\[
s \geq 0
\]

### Calculation for a 4-ft Side Length
Now, we can calculate the number of carrots that can be planted in a garden with a side length of 4 feet. We substitute \( s = 4 \) into the function:

\[
f(4) = 9(4^2) = 9(16) = 144
\]

Thus, the students can plant **144 carrots** in a garden that is square with 4-ft side lengths.