Approximate the population of the bacteria 20 minutes from now.

Question

The current population of a certain bacteria is 6,416 organisms. It is believed that the bacteria's population is tripling every 10 minutes. Approximate the population of the bacteria 20 minutes from now. Round to nearest whole number.

Answer 1

Hi Joshua,

So, this is a relationship that can be modeled by the following exponential equation (where the variable t is defined as time in minutes, and the output P(t) would give the population growth at time = t):

P(t) = 6,416(3)^t/10

Here, you can see that at present (or t = 0), the population P(t) would evaluate to 6,416 organisms:

P(t) = 6,416(3)^0/10 = 6,416(3)⁰ = 6,416

And at t = 10, the original population would triple (6,416×3), as given in the problem statement:

P(t) = 6,416(3)^10/10 = 6,416(3)¹ = 19,248

Therefore, 20 minutes from now, we can use the model to evaluate what the population would be at t = 20:

P(t) = 6,416(3)^20/10 = 6,416(3)² = 57,744 organisms

Best,

Todd

Answer 2

In 20 minutes it triples twice, or nine time the original. What is that number?