How long will it take for $2000 to double if it is invested at 6.25% interest compounded continuously? can some show me how to set this problem into this equation A=Pe^rt, please!

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- Mertsj

\[4000=2000e ^{.0625t}\]

- Mertsj

\[2=e ^{.0625t}\]

- Mertsj

\[\ln 2=.0625t(\ln e)\]

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## More answers

- Mertsj

\[\frac{\ln2}{.0625}=t\]

- Mertsj

\[11.09 yrs = t\]

- anonymous

can you please give me a crash course on what you did, Please...

- Mertsj

Did you understand how the values were substituted into the equation?

- anonymous

no i didnt

- Mertsj

A is the amount which was determined to be $4000 because the problem asked how long it would take a $2000 investment to double.

- Mertsj

If $2000 doubles, it will then be $4000 would you agree?

- Mertsj

So the problem is really asking "how long will it take $2000 to turn into $4000"

- anonymous

what does the e stand for?

- Mertsj

The e is a frequently used mathematical constant. It doesn't stand for anything. It is sort of like pi. Just a commonly used constant. It is part of the formula just like pi is when you write

- Mertsj

\[A=\pi r^2\]

- Mertsj

You don't replace pi with anything and you don't replace e with anything.

- anonymous

can you help me figure out another problem but let me do it and maybe you can coach me.

- Mertsj

It's numerical value (if you must know) is 2.718281828...

- Mertsj

ok

- Mertsj

Lay it on me.

- anonymous

What rate of interest compounded continuously is needed for an investment of $500 to grow to $900 in 10 years?

- Mertsj

What is A?

- anonymous

900

- Mertsj

What is P?

- anonymous

500

- Mertsj

What is t?

- anonymous

10

- Mertsj

What are you trying to find?

- anonymous

the rate of interest

- Mertsj

Yes. r

- Mertsj

So plug everything in.

- anonymous

900=500e^r10

- Mertsj

\[900=500e ^{10r}\]

- Mertsj

Divide both sides by 500

- anonymous

ok

- anonymous

In1.8=e^10r

- Mertsj

\[1.8=e ^{10r}\]

- Mertsj

Now when you take the natural log of both sides it should look like this:
\[\ln 1.8=\ln e ^{10r}\]

- anonymous

ok

- Mertsj

Now bring the exponent down using the third law of logs and get this

- Mertsj

\[\ln 1.8=10r \ln e\]

- Mertsj

But of course ln e = 1 so we have:

- Mertsj

\[\ln 1.8=10r\]

- Mertsj

So just divide both sides by 10 and you are done

- anonymous

0.18=r

- Mertsj

\[\frac{\ln 1.8}{10}=r=.05878=5.88 %\]

- Mertsj

Did you take the natural log of 1.8 before you divided by 10?

- anonymous

no

- Mertsj

Do you now how to do that?

- anonymous

no

- Mertsj

You do understand that it says ln 1.8 divided by 10?

- Mertsj

Do you have a scientific calculator?

- anonymous

yes

- Mertsj

Can you find the ln button?

- Mertsj

It's probably right next to the log button

- anonymous

yes i just pressed it and got the same as you did do i now dive that by 10

- Mertsj

Yes

- Mertsj

Now multiply by 100 to change it to percent.

- anonymous

got it you just answered my question!! thank you so much Mertsj

- Mertsj

You're welcome and good luck. Isn't learning fun???!!!

- anonymous

yeah your the best!!!!!

- Mertsj

Thanks.

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