SOLUTION: Please help! Do not understand at all! If interest is compuonded continuously, after t years the amount in the account is A=Pe^rt (where A=total amount, P=original amount.invest

Question 797634: Please help! Do not understand at all!
If interest is compuonded continuously, after t years the amount in the account is A=Pe^rt (where A=total amount, P=original amount.invested, and r=interest rate).
1) how long does it take for your investment to double at 4% interest? (Round to nearest year) hint: if your original amount is x, the doubled amount is....
2) How long does it take for your investment to teiple at 4% interest? (round to nearest year)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
If interest is compuonded continuously, after t years the amount in the account is A=Pe^rt (where A=total amount, P=original amount.invested, and r=interest rate).
1) how long does it take for your investment to double at 4% interest? (Round to nearest year) hint: if your original amount is x, the doubled amount is....
2) How long does it take for your investment to teiple at 4% interest? (round to nearest year)
***
A=Pe^rt
A/P=e^rt
To double investment:
A/P=2
e^rt=2
e^.04t=2
take log of both sides
.04t*lne=ln2
lne=1
t=ln2/.04≈17 yrs
..
To triple investment:
A/P=3
e^rt=3
e^.04t=3
take log of both sides
.04t*lne=ln3
lne=1
t=ln3/.04≈24 yrs

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