A certain bacteria population is known to quadruples every 150 minutes. Suppose that there are initially 200 bacteria.

What is the size of the population after t hours?

This is a geometric progression

The size of the population afeter t hours will be=a₁*r^n

a₁ = the first term = 200

r=common ratio=4

150 minutes=150 minutes * (1 hour / 60 minutes) = 2.5 hours.

In this case:

the size of the populatation after t hours=200*4^t/2.5=200*4^0.4t

To check

t=0⇒ the size will be=200*4⁰=200*1=200

t=2.5 hours=150 minutes; the size will be = 200*4¹=800

t=5 hours; the size will be=200*4²=200*16=3200

Answer: the size will be = 200*4^ (0.4t)