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?

approximately 78 years

Step-by-step 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