Question

Addison painted her room. She had 505050 square meters to paint, and she painted at a constant rate. After 222 hours of painting, she had 353535 square meters left.

Answer 1

Answer:

A(t) = -(15/2)t + 50

Step-by-step explanation:

First, let me complete the question for you, cause there are a missing part here:

Addison painted her room. She had 50 square meters to paint, and she painted at a constant rate. After 2 hours of painting, she had 35 square meters left. Let A(t), denote the area to paint A (measured in square meters) as a function of time t (measured in hours).

According to the question, we want an expression as a function that explains the rate of painting of Addison. It states that is painting at a constant rate, therefore, we can assume that is a linear function (Cause is constant with time)

The expression for a linear function is:

y = mx + n    (1)

So, If A(t) is the area to paint, we know that at the beggining, before it began the painting we have the whole 50 m² to paint, and hence, we can assume that at time 0 h, we have left to paint 50 m².

After t = 2h, 35 m² were left unpainted, so in order to write an function we need a slope and a interception in y axis. to get the slope we apply the following expression:

m = y₂ - y₁ / x₂ - x₁  (2)

We have two points, so we can use them to  get the slope:

Point 1: (0, 50);   Point 2: (2, 35)

m = 35 - 50 / 2 - 0

m = -15/2 or -7.5

Now that we have the slope, let's get interception n:

50 = -7.5(0) + n

50 = n

Hence, the expression to this painting rate will be:

A(t) = -(15/2)t + 50

A(t) = -7.5t + 50

You can use any of these two.

Hope this helps