If $ 2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $ 5000 at 3%? Round to the nearest tenth. Can someone please show meall the steps to solve.

Question

If $ 2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $ 5000 at  3%? Round to the nearest tenth.      Can someone please show meall the steps to solve.

anonymous · Answer

Use the formula 
A= Pe^rt

anonymous · Answer

P=2500
r=.03
A=5000

anonymous · Answer

your job is to solve 
$$5000=2500e^{.03t}$$ for t. can you do that?
 first step is divide by 2500
second is to take the log
third is to divide by .03

anonymous · Answer

i can write it if you like

anonymous · Answer

did you get it?

amistre64 · Answer

how long does it take to double :)

anonymous · Answer

yes please show me, not sure what log third is?

amistre64 · Answer

ln(2)/r i beleive

anonymous · Answer

ok start with dividing by 2500 and get 
$$2=e^{.03t}$$ take the log get 
$$\ln(2)=.03t$$ and then divide by .03 get 
$$t=\frac{\ln(2)}{.03}$$ then a calculator

anonymous · Answer

"take the log" is shorthand for "write in equivalent logarithmic form"

amistre64 · Answer

ln(n-tuple)/r  is the basic formula

anonymous · Answer

what amistre said.  point is that the initial amount was half the final amount, so you were answering the question "how long before your money doubles?"

anonymous · Answer

if you invest $2,500 and amistre invests 10, 000,000 and i invest $12.50 the doubling time is still the same

anonymous · Answer

ok I think i got it. thanks