A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle.
As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size?
So we know that the formula for the area of a rectangle is . Now both the length and width of the rectangle increase at 3 km/s, therefore, . We want to know the time when the area is four times its original area, therefore, our new formula is: . Plugging in our known values we have:
The area is four times its original area after <span>\frac{4}{3} s[/tex]</span>.