anonymous
  • anonymous
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!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Mertsj
  • Mertsj
\[4000=2000e ^{.0625t}\]
Mertsj
  • Mertsj
\[2=e ^{.0625t}\]
Mertsj
  • Mertsj
\[\ln 2=.0625t(\ln e)\]

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Mertsj
  • Mertsj
\[\frac{\ln2}{.0625}=t\]
Mertsj
  • Mertsj
\[11.09 yrs = t\]
anonymous
  • anonymous
can you please give me a crash course on what you did, Please...
Mertsj
  • Mertsj
Did you understand how the values were substituted into the equation?
anonymous
  • anonymous
no i didnt
Mertsj
  • 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
  • Mertsj
If $2000 doubles, it will then be $4000 would you agree?
Mertsj
  • Mertsj
So the problem is really asking "how long will it take $2000 to turn into $4000"
anonymous
  • anonymous
what does the e stand for?
Mertsj
  • 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
  • Mertsj
\[A=\pi r^2\]
Mertsj
  • Mertsj
You don't replace pi with anything and you don't replace e with anything.
anonymous
  • anonymous
can you help me figure out another problem but let me do it and maybe you can coach me.
Mertsj
  • Mertsj
It's numerical value (if you must know) is 2.718281828...
Mertsj
  • Mertsj
ok
Mertsj
  • Mertsj
Lay it on me.
anonymous
  • anonymous
What rate of interest compounded continuously is needed for an investment of $500 to grow to $900 in 10 years?
Mertsj
  • Mertsj
What is A?
anonymous
  • anonymous
900
Mertsj
  • Mertsj
What is P?
anonymous
  • anonymous
500
Mertsj
  • Mertsj
What is t?
anonymous
  • anonymous
10
Mertsj
  • Mertsj
What are you trying to find?
anonymous
  • anonymous
the rate of interest
Mertsj
  • Mertsj
Yes. r
Mertsj
  • Mertsj
So plug everything in.
anonymous
  • anonymous
900=500e^r10
Mertsj
  • Mertsj
\[900=500e ^{10r}\]
Mertsj
  • Mertsj
Divide both sides by 500
anonymous
  • anonymous
ok
anonymous
  • anonymous
In1.8=e^10r
Mertsj
  • Mertsj
\[1.8=e ^{10r}\]
Mertsj
  • Mertsj
Now when you take the natural log of both sides it should look like this: \[\ln 1.8=\ln e ^{10r}\]
anonymous
  • anonymous
ok
Mertsj
  • Mertsj
Now bring the exponent down using the third law of logs and get this
Mertsj
  • Mertsj
\[\ln 1.8=10r \ln e\]
Mertsj
  • Mertsj
But of course ln e = 1 so we have:
Mertsj
  • Mertsj
\[\ln 1.8=10r\]
Mertsj
  • Mertsj
So just divide both sides by 10 and you are done
anonymous
  • anonymous
0.18=r
Mertsj
  • Mertsj
\[\frac{\ln 1.8}{10}=r=.05878=5.88 %\]
Mertsj
  • Mertsj
Did you take the natural log of 1.8 before you divided by 10?
anonymous
  • anonymous
no
Mertsj
  • Mertsj
Do you now how to do that?
anonymous
  • anonymous
no
Mertsj
  • Mertsj
You do understand that it says ln 1.8 divided by 10?
Mertsj
  • Mertsj
Do you have a scientific calculator?
anonymous
  • anonymous
yes
Mertsj
  • Mertsj
Can you find the ln button?
Mertsj
  • Mertsj
It's probably right next to the log button
anonymous
  • anonymous
yes i just pressed it and got the same as you did do i now dive that by 10
Mertsj
  • Mertsj
Yes
Mertsj
  • Mertsj
Now multiply by 100 to change it to percent.
anonymous
  • anonymous
got it you just answered my question!! thank you so much Mertsj
Mertsj
  • Mertsj
You're welcome and good luck. Isn't learning fun???!!!
anonymous
  • anonymous
yeah your the best!!!!!
Mertsj
  • Mertsj
Thanks.

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