Amusement Park Food Supply math question

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) Writing equations here can be tricky.

Your food supply equation will use y = mx + C. What is your m here and what is your C?

For park attendance, this one's a little trickier and uses exponents. It might look something like y = C (r) ^ x. Try to think about what makes sense for C, r, and x here.

b) A shortage of food will happen when park attendance becomes greater than food supply. At what point will park attendance *grow* to become greater than food supply? In terms of graphs, this happens when the lines intersect each other.

How do you figure out where the lines intersect? Set the equations equal to each other, and solve for x.

c) & d) These questions ask you to change your equations a bit and look at the results. c) asks you to double your value for C, and d) asks you to double your value for m and C.

Good luck!