I don't want the answer here so much as an explanation as to instructions explaining how to get there :
the population of a colony of bacteria grows exponentially according to the function below (included in a minute), where t is the time in hours. How long until the population is 1000?

Question

I don't want the answer here so much as an explanation as to instructions explaining how to get there : 
 the population of a colony of bacteria grows exponentially according to the function below (included in a minute), where t is the time in hours. How long until the population is 1000?

anonymous · Answer

$$b(t) = 12e^.2t$$ (the t is part of the exponent but the formatting won't let me do that)

anonymous · Answer

so to get there, substitute b(t) with 100. so it looks like 1000=12e to the 2nd power multiplied by the t as a power $$1000=12e ^{2t}$$ 
then you divide both sides by 12$$83.333333=e ^{2t}$$
e is just a constant. which is 2.71828
so you get $$83.333333=2.71828^{2t}$$
which means you need to square root both sides.
$$\sqrt{83.333333}=2.71828^{t}$$
which equals to $$9.1287092734953499558532073114273$$ but we will round to 9.1287
$$9.1287=2.71828^{t}$$
then you use the log formula-> 
$$\log_{2.71828}9.1287=t$$
which means $$\log_{91287} / \frac{ \log _{10}9.1287 }{ \log _{10} 2.71828 }$$
and the answer is 2.2114247842569241065266455869202 hours. or 2.2 hours

anonymous · Answer

Shouldn't this be posted in maths

anonymous · Answer

it's a written explanation, so it DOES count as writing