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 supply grow linearly F = F₀+ .2t where F is supply in millions. and t is in years

Attendance grows exponentially A = A₀(1 +.03)^t

B) Solve for t where F = A You can write as G = F-A and solve for t's where G is 0 numerically or graphically.

C) Just redo the analysis for twice F₀. The exponential always will pass the linear function as t grows. It will just be later.

D) Again, redo calculation for twice F₀ and .4 instead of 2. Again, the exponential must catch up.