Amusement Park Food Supply

Question

The annual attendance at the amusement park is initially 2 million people and is increasing at 3% per year. The park’s annual food supply is initially adequate for 4 million people and is increasing at a constant rate adequate for an additional 0.2 million people per year.

a. Write the equation that represents the food supply. Write the equation represents the park attendance.

b. Based on these assumptions, in approximately what year will the amusement park first experience shortages of food?

c. If the park doubled its initial food supply and maintained the rate of increase of 0.2 million people per year, would shortages still occur? In approximately which year?

d. If the park doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur? After how many years would the food supply run out?

Answer 1

a)

Food: f(x) = 4+.2x

Attendance: a(x) = 2(1+0.03)^x

b) One way of solving this is to graphically find the point of intersection where

a(x) >= f(x)

Using Desmos, this intersection point is (76.797, 19.359). So ≈ 77 years from now, there will be shortages.

c) Yes, in ≈ 86 years from now per Desmos plot.. (f(x) = 4+0.4x)

d) Yes, in ≈ 110 years from now. (f(x) = 8+0.4x)