SOLUTION: THE AMOUNT A IN AN ACCOUNT AFTER t YEARS FROM AN INITIAL PRINCILE P INVESTED AT AN ANNUAL RATE r COMPOUNDED CONTINUOUSLY IS GIVEN BY A=Pe^rt WHERE r IS EXPRESSED AS A DECIMAL. HOW

Algebra ->  Points-lines-and-rays -> SOLUTION: THE AMOUNT A IN AN ACCOUNT AFTER t YEARS FROM AN INITIAL PRINCILE P INVESTED AT AN ANNUAL RATE r COMPOUNDED CONTINUOUSLY IS GIVEN BY A=Pe^rt WHERE r IS EXPRESSED AS A DECIMAL. HOW      Log On


   

Question 64971: THE AMOUNT A IN AN ACCOUNT AFTER t YEARS FROM AN INITIAL PRINCILE P INVESTED AT AN ANNUAL RATE r COMPOUNDED CONTINUOUSLY IS GIVEN BY A=Pe^rt WHERE r IS EXPRESSED AS A DECIMAL. HOW MANY YEARS WILL IT TAKE AN INITIAL INVESTMENT OF $1,000 TO GROW TO $1,700 AT THE RATE OF 4.42% COMPOUNDED CONTINUOUSLY?
Answer by funmath(2933) About Me  (Show Source):
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THE AMOUNT A IN AN ACCOUNT AFTER t YEARS FROM AN INITIAL PRINCILE P INVESTED AT AN ANNUAL RATE r COMPOUNDED CONTINUOUSLY IS GIVEN BY A=Pe^rt WHERE r IS EXPRESSED AS A DECIMAL. HOW MANY YEARS WILL IT TAKE AN INITIAL INVESTMENT OF $1,000 TO GROW TO $1,700 AT THE RATE OF 4.42% COMPOUNDED CONTINUOUSLY?
A=1700
P=1000
r=4.42/100=.0442
1700=1000e%5E%28.0442t%29
1700%2F1000=1000e%5E%28.0442t%29%2F1000
17%2F10=e%5E%28.0442t%29
ln%2817%2F10%29=ln%28e%5E.0442t%29
ln%2817%2F10%29=.0442tln%28e%29
ln%2817%2F10%29=.0442t%281%29
ln%2817%2F10%29=.0442t
ln%2817%2F10%29%2F.0442=.0442t%2F.0442
ln%2817%2F10%29%2F.0442=t
12.00516405=t
highlight%28t=12%29 yrs.
Happy Calculating!!!