Question

The area, A, of a forest, in acres, is modeled by the equation

A = 5,000 · ()" where d is the number of decades since the beginning of
the year 1950.
a. Is the area of the forest increasing or decreasing with time? Explain how
you know.
b. What was the area of the forest in 1950?
c. What was the area of the forest in 1940?

Answer 1

The area of the forest is increasing with time. The area of the forest in 1950 was 25,000 acres. The area of the forest in 1940 was 20,000 acres.

Step-by-step explanation:

a. The area of the forest is increasing with time because the equation A = 5,000 · (d+5) represents a linear function where the coefficient of d is positive. This means that as the number of decades since 1950 increases, the area of the forest also increases.

b. To find the area of the forest in 1950, we need to substitute d=0 into the equation. A = 5,000 · (0+5) = 5,000 · 5 = 25,000 acres.

c. To find the area of the forest in 1940, we need to determine the number of decades since 1950. Since 1940 is 10 years before 1950, we can substitute d=-1 into the equation. A = 5,000 · (-1+5) = 5,000 · 4 = 20,000 acres.