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