Math Question?

Question

Each person eats one unit of food only. So one food can support one person. If food is growing at an arithmetic rate of 100*X and the population is growing at the rate of 2 power x. Where X is the number of years. How many years before food production can not support the population?

Answer 1

You want to find the value of x (the number of years) for which the amount of food units becomes less than the population at that time. So we want to find the x for which
100x = 2^x
After that, 100x < 2^x because the exponent will be growing bigger.

Unfortunately there's no real analytical way to solve this. You could use an interative method like Newton's method, or some other way of getting an approximate answer. In this case you could take the log (base 2) of both sides and get log [base 2] (100x) = x, and recursively plug in answers.

Alternatively, if we just want to get things to the nearest integer, we can use some trial and error. Notice that 100*10 = 1000 and 2^10 = 1024, while 100*9 = 900 and 2^9=512, so the answer is somewhere between 9 and 10 years.

Answer 2

In 10 years the population will have grown 1024 times, and the food supply will have grown only 1000 times. So just less than 10 years would be required.