Bacteria population growth: what am I missing?

Question

I am having a confusion while solving the problem below.

Under ideal conditions, a certain bacteria population is known to double every three hours. Suppose that initially there are $100$ bacteria.

1. What is the size of the population after $15$ hours?

2. What is the size of the population after $t$ hours?

Here, I put the population function as $$P(t) = 100 \left(\frac{5}{3}\right) t$$ since the population grows to $\frac{5}{3}$ of its original value every hour. (I think there is an error here, but I don't know what is wrong with it.) When I calculate $P(15)$ to solve for question 1, I keep on getting $2500$ when the answer should be $3200$. How can this be?

Answer 1

Try this formula (because the population doubles over a certain time period, it will be power of $2$): $P(t)=100\cdot 2^{\frac{t}{3}}$