SOLUTION: Can someone please try and solve this by 11:59pm TONIGHT!!! Or I will not receive credit at all even for trying and still getting the wrong answer!!!I can't figure this out, my fr

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Can someone please try and solve this by 11:59pm TONIGHT!!! Or I will not receive credit at all even for trying and still getting the wrong answer!!!I can't figure this out, my fr      Log On


   

Question 126672: Can someone please try and solve this by 11:59pm TONIGHT!!! Or I will not receive credit at all even for trying and still getting the wrong answer!!!I can't figure this out, my friend and both got 6.88 years for part B. But my instructor says its incorrect. THANKS SO MUCH!!
A) If a bank compounds continuously, then the formula used is A=Pe%5Ert
where e is a constant and equals approximately 2.7183.
Calculate A with continuous compounding. Round your answer to the hundredth's place.
Answer:
Show work in this space:
B) A commonly asked question is, “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.
Answer:
Show work in this space:

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
A=Pe%5E%28rt%29

We want to double the amount represented by P, so A needs to equal 2P

2P=Pe%5E%28rt%29
e%5E%28rt%29=2

Now, take the natural log of both sides:
log%28e%2Ce%5E%28rt%29%29=log%28e%2C2%29

rt%2Alog%28e%2Ce%29=log%28e%2C2%29, but log%28e%2Ce%29=1 so,

rt=log%28e%2C2%29

t=log%28e%2C2%29%2Fr

For a rate of 8% (0.08), the calculator says:
t=8.66 years.

Sanity check: Use the rule of 72. Divide 72 by the interest rate in whole numbers to get the approximate number of years for your money to double. 72%2F8=9. 8.66 and 9 are pretty close, so that gives me high confidence in the answer.