Creating Expression

Question

A certain bacteria population is known to triple every hour. Suppose that there are initially 150 bacteria. 

What is the size of the population after t hours?

Answer 1

This would be an exponential equation because the population is growing by 3 times the current population every hour. So, that would mean the population with respect to time, P(t), would be 150•3^t where "t" represents time in hours. Initially, when t = 0, P(0) = 150•3⁰ = 150•1 = 150. Then after 1 hour, the population P(1) = 150•3¹ = 150•3 = 450. After two hours, P(2) = 150•3² = 150•9 = 1350 (which is triple the 450 from the previous hour).

So, the size of the population after "t" hours is 150•3^t or P(t) = 150•3^t