Question

the gardening club is constructing a stone retaining wall on a sloped area near the school. the function below describes the height of the wall from the ground, in feet, based on the number of days, x, the club has been working on it.\\( f(x) = 1.25x + 2.5 \\)\
two members of the gardening club determined the height of the wall based on a given number of days. their work is shown below.\
joanne\
\\( 5 = 1.25x + 2.5 \\)\
\\( x = 2 \\)\
marcus\
\\( f(5) = 1.25(5) + 2.5 \\)\
\\( = 8.75 \\)\
which student is correct and why?\
a. marcus is correct because \\( f(5) = 8.75 \\) reveals that the input of 8.75 feet will show that 5 days have elapsed.\
b. joanne is correct because \\( f(x) = 5 \\); \\( x = 2 \\) reveals that the output of 5 days will show a height of 2 feet.\
c. joanne is correct because \\( f(x) = 5 \\); \\( x = 2 \\) reveals that the output of 2 feet will show that 5 days have elapsed.\
d. marcus is correct because \\( f(5) = 8.75 \\) reveals that the input of 5 days will show a height of 8.75 feet.

Explanation:

Step1: Analyze the function

The function is \( f(x) = 1.25x + 2.5 \), where \( x \) is the number of days and \( f(x) \) is the height of the wall.

Step2: Evaluate Marcus's calculation

Marcus calculates \( f(5) \):

$$ f(5)=1.25(5)+2.5 = 6.25 + 2.5=8.75 $$

This means when \( x = 5 \) (5 days), the height \( f(5) \) is 8.75 feet. His reasoning says \( f(5) = 8.75 \) reveals that 5 days give a height of 8.75 feet, which is correct.

Step3: Evaluate Joanne's calculation

Joanne solves \( 5=1.25x + 2.5 \):

$$ 1.25x=5 - 2.5=2.5\\ x=\frac{2.5}{1.25}=2 $$

This means when \( f(x)=5 \) (height is 5 feet), \( x = 2 \) (2 days). But the question is about the height based on days, so Marcus's approach (finding height for a given day) is correct for interpreting the function's meaning here.

Answer:

D. Marcus is correct because \( f(5) = 8.75 \) reveals that the input of 5 days will show a height of 8.75 feet.