Question

In art class Tico is copping a detail from a painting. He paints slowly for the first few days, but manages to increase his rate after that. The graph shows his progress after he increased his rate. How many square centimeters of his painting will he finish in 7 days after the increase in rate?He will finish___cm^2 of his painting in 7 days after the increase in rate.

Answer 1

In order to determine the area painted by Tico after 7 days of the increase rate, consider that the relation between area and days after the increase rate can be model by a linear equation (as you can notice in the given graph).

Let A the area and d the days, then, you can write, in a general way:

A - Ao = m(d - do)

where m is the slope of the line and (do,Ao) is any point on the line.

To find the value of m, use:

`m=(A_2-A_1)/(d_2-d_1)`

where (d1,A1) and (d2,A2) are any two points on the line. For instance, use:

(d1,A1) = (3,175)

(d2,A2) = (8,400)

Replace the previous values into the expression for m and simplify:

`\begin{gathered} m=(400-175)/(8-3) \\ m=(225)/(5)=45 \end{gathered}`

Now, use (do,Ao) = (3,175) and m=45 into the general equation of a line and solve for A:

A - 175 = 45(d - 3)

A - 175 = 45d - 135

A = 45d - 135 + 175

A = 45d + 40

Now, replace d = 7 into the previous equation:

A = 45(7) + 40

A = 315 + 40

A = 355

Hence. after 7 days of the increase in rate, the area painted by Tico is 355 cm^2