Question

6 A population of bacteria is doubling every year. Initially the population has 500 bacteria. (a) Write an equation to model this scenario using the variables y and x. (b) What will the population of bacteria be after 2 years?

Answer 1

Let the population of bacteria at any time be y, and the time in years to be x

We have a geometric progression with common ratio 2

our general equation would be

$y=500(2)^x$

b. after 2 years, the bacteria population would be

$y=500(2)^2=2000\text{ bacteria}$