Dear Math Help Forum, How long will it take to double?

[Kataangel]

Hi I'm stuck on this question:

An investment grows at a continuous 12% rate per year. In how many years will the value of the investment double?

I'm getting a weird decimal number .776

Can anyone suggest a method I can use to calculate the time of a continuously growing investment?

Thanks,
Kataangel

[jeneverboy]

Try to make a formula for it, like

For instance you have 100 dollar

after one year you will have; 100*1.12 = 112
after two years you will have; 112*1.12 = 100*1.12*1.12= 100* (1.12)^2=...

after x years you will have; 100*(1.12)^x=....

Now you have to end with 200 dollars in this case. Can you finish the formula?

[stapel]

Use the continuously-compounded formula they gave you. Whatever the original amount P was, you are given that A = 2P, so just use P = 1 and A = 2. Plug in the value they've given you for r (or k). Then solve for t.