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 .5 million people per year. What year will they have food shortages?

78.32 years later

Step-by-step explanation:

 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 steady rate adequate for .5 million people per year. In what year will you have food shortages?

The first thing is to get the equations that each case represents:

The population tells us that it increases its initial population each year by 4%, that is, it would be multiplied by 1.04 in each year, therefore it would look like this:

P (t) = 2 * (1.04) ^ t

Now for annual food supply it has the following function, because it increases by a fixed value, and it also increases by a fixed value but with the time variable, it would be as follows:

F (t) = 4 + 0.5 * t

To know when there is a shortage of food, is when the quantity of both is equal, because the food would be fully written. That is, we look for the intersection of both functions.

Therefore we turn to the page of https://en.symbolab.com/graphing-calculator

Where we graph both functions and here the intersection tells us.

It does not show that at t = 78.32 years, the functions are equalized and from that point the shortage begins.

i hope this is what you were looking for.

see attached graph