Question

A certain bacteria population is known to triple every 90 minutes. Suppose that there are initially 80 bacteria.

What is the size of the population after t hours?

Answer 1

If you know the doubling formula, you can just convert
\[P2^{t/k} \to P3^{t/k} \] and use it that way.

Answer 2

So if this was doubling instead of tripling you would have
\[P(t) = (80)2^{t/90}\] since you want this with respect to hours and not minutes you would convert the 90 minutes to hours or 1.5
so
\[P(2) = 80 \times 2^{t/1.5}\]
Now just convert this to tripling instead of doubling.

Answer 3

And that should be P(t) not P(2). Sorry.

Answer 4

No idea what that is...its online homework. I think im supposed to use

A(t)=(A_0)e^(kt)

Answer 5

\[A(t)=A _{0}e ^{kt}\]

Answer 6

You can use that equation if you want to. It's just harder and more difficult. If, however, there is a population whose growth doubles for a given time span, you can represent the growth by
\[A(t) = A_0 2^{t/k}\] where k represents the time it takes to "double". If it was tripling every time span you would use a 3 instead of a 2.