Question

Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A(t) denote the area to paint A (measured in square meters) as a function of time t (measured in hours).

Answer 1

Answer: $A(t)=-8t+52$

Step-by-step explanation:

The missing question is: "What is the Functions formula A(t)=?"

<h2 />

The  equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

According to the data given in the exercise, you know that:

- $A(t)$ represents the area to paint the Hiros' romm as a function of time.

- The rate he painted the room was 8 square meters per hour.

- The area left to paint after 3 hours was 28 m².

Therefore, based on this, you can idenfity that:

1. The slope of the line is:

$m=-8$

2. One of the point on the line is:

$(3,28)$

So you must substitute the slope and the coordinates of that point into $y=mx+b$ and then solve for "b" in order to find its value:

$28=-8(3)+b\\\\28+24=b\\\\b=52$

Therefore, you can determine that the function $A(t)$ is:

$A(t)=-8t+52$