An investment in a savings account grows to three times the initial value after t years.

If the rate of interest is 5%, compounded continuously,

Question

An investment in a savings account grows to three times the initial value after t years.




If the rate of interest is 5%, compounded continuously,

zepdrix · Answer

Hey Shan :)
Welcome to OpenStudy!

Is that the entirety of the question?
Seems like we're missing something, hmm

ineedhelplz · Answer

Yes, it does...

shanmarie745 · Answer

that is the whole question. trying to solve for t

zepdrix · Answer

Ohh I see :)
Ok ok ok, brb

zepdrix · Answer

So we're given that:
Our rate of interest is 5%: $\rm r=.05$
Our starting amount is some unknown $\rm P$
our ending amount is triple our starting amount $\rm 3P$

And we're using continuous compounding,$$\large\rm A=Pe^{rt}$$

zepdrix · Answer

So we'll plug in the information,$$\large\rm 3P=Pe^{.05t}$$And solve for t.

zepdrix · Answer

Divide both sides by P,$$\large\rm 3=e^{.05t}$$Take natural log of both sides to deal with the exponential base.

zepdrix · Answer

Bahh you went offline >.<
Ok lemme know if you come back and still need assistance.