The population of a certain bacteria can multiply threefold in 24 hours. If there are 500 bacteria now, how many will there be in 96 hours? The population of a certain bacteria can multiply threefold in 24 hours. If there are 500 bacteria now, how many will there be in 96 hours?
I figured out this bacteria $=500(3)^{96/24}$
but then my mate told me it's bacteria $=500(1+3/1)^{96/24 }$
what do I do what is the next step.
 A: It depends on the intended meaning of multiply threefold. You’re interpreting it as meaning increase by a factor of $3$, which is how I would interpret it. Your mate is interpreting it to mean that the amount by which the population increases is $3$ times the present population; I would call that a fourfold increase. However, I can imagine someone using the term multiply threefold in that way; the only way to be certain what’s intended is to ask the person who set the problem.
A: Your mate is simply wrong. I see no ambiguity here at all.
A: Regardless of the ambiguity, that solution doesn't look right because that doesn't seem like the right rate constant. In order to solve an exponential growth problem we normally assume a growth given by
$$ P(t) = P(0) e ^{k t}$$
We can find k by using the given information (there is where the ambiguity lies, I agree that threefold prabably means 3 times the present value like the rest).
If we then use that 
$$P(24) = 3 P(0) = P(0) e ^{k 24}$$
we can then find k and the problem will be a little easier, since once we have k we can then find $P(t)$ for any future value of $t$.
