# Math Help - log question

1. ## log question

Hi
I need help on the following question:

If prices are increasing at the rate of 7.8% per year write down an equation for prices as a function of time. How long does it take for prices to double? How long does it take for prices to treble?

I have found the equation:
$P = Po(1+\frac{7.8}{100})^t$

To find t i transpose the equation to get:
$\frac{log(P)-log(Po)}{log(1.078)}=t$

now i don't know how to find how long does it take for prices to double or treble, because what will the values be for P and Po?

P.S

2. Hello, Paymemoney!

Your work is correct . . .

$\text{I would write it like this: }\;t \:=\:\frac{\log\left(\dfrac{P}{P_o}\right)}{\log(1 .078)}$

If the price doubles, then $P$ will be twice the initial price $P_o.$

. . Hence: . $\frac{P}{P_o} \:=\:2$

Got it?

3. yep thanks i get it.