Find the amount of time required for an amount to double at the given rate if the interest is compounded continuously. Problem--- 5%

Question

Find the amount of time required for an amount to double at the given rate if the interest is compounded continuously. Problem---> 5%

tkhunny · Answer

$e^{0.05\cdot t} = 2$ - Solve for t.

anonymous · Answer

can you explain ? @tkhunny

tkhunny · Answer

I already did.  Have you used logarithms?  That's all you need.

anonymous · Answer

yes , but how would i solve for t?

anonymous · Answer

@zaynahf

tkhunny · Answer

Seriously, use logarithms.

tkhunny · Answer

Base 'e' logarithms?  Natural logs?  Let's see what you get.

anonymous · Answer

plug in e^0.05 into my calculator ?

anonymous · Answer

@zaynahf

tkhunny · Answer

You did say that you had used logarithms.  It appears this is not the case.

If: $e^{0.05t} = 2$

Then: $\ln\left(e^{0.05t}\right) = \ln(2)$

Further: $0.05\cdot t\cdot\ln(e) = \ln(2)$

Finally: $0.05\cdot t = \ln(2)$

anonymous · Answer

Then divide both sides by 0.05 ?

anonymous · Answer

=13.863?

tkhunny · Answer

That's it.  good work.

Let's try another one so I can see you deal with the logarithms.

anonymous · Answer

okay.