Question

1. joey enlarged a 3 - inch by 5 - inch photograph on a copy machine. he enlarged it four times. the table below shows the area of the photograph after each enlargement.

enlargement	0	1	2	3	4

what is the average rate of change of the area from the original photograph to the fourth enlargement, to the nearest tenth?
(1) 4.3
(2) 4.5
(3) 5.4
(4) 6.0

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( y = f(x) \) from \( x = a \) to \( x = b \) is given by \( \frac{f(b)-f(a)}{b - a} \). Here, the "x" values are the enlargement number (0 for original, 4 for the fourth enlargement) and the "y" values are the area. So we need to find \( \frac{\text{Area at enlargement } 4 - \text{Area at enlargement } 0}{4 - 0} \).

Step2: Identify the values

From the table, the area at enlargement 0 (original) is 15 square inches, and the area at enlargement 4 is 36.6 square inches. The number of enlargements from 0 to 4 is \( 4 - 0=4 \).

Step3: Calculate the average rate of change

Substitute the values into the formula: \( \frac{36.6 - 15}{4 - 0}=\frac{21.6}{4} = 5.4 \).

Answer:

(3) 5.4