Question

The population of a country is initially 2 million people and is increasing at 4% per year. The country's annual food supply is initially adequate for 4 million people and is increasing at a constant rate adequate for an additional 0.5 million people per year. Based on these assumptions, in approximately what year will this country first experience shortages of food?

Answer 1

approximately 78 years

Explanation:

Population

y =ab^t where a is the initial population and b is 1+the percent of increase

t is in years

y = 2000000(1+.04)^t

y = 2000000(1.04)^t

Food

y = a+bt where a is the initial population and b is constant increase

t is in years

b = .5 million = 500000

y = 4000000 +500000t

We need to set these equal and solve for t to determine when food shortage will occur

2000000(1.04)^t= 4000000 +500000t

Using graphing technology, (see attached graph The y axis is in millions of years), where these two lines intersect is the year where food shortages start.

t≈78 years