SOLUTION: How many years will it take for a $100 investment to grow to $700 if it is compounded continuously at a rate of 9%? A(t)= P*e^rt

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Question 703336: How many years will it take for a $100 investment to grow to $700 if it is compounded continuously at a rate of 9%?
A(t)= P*e^rt
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

A=Pe%5E%28rt%29 Start with the continuous compounding formula.


700=100%2Ae%5E%280.09%2At%29 Plug in A=700, P=100, and r=0.09 (the decimal equivalent of 9%).


700%2F100=e%5E%280.09%2At%29 Divide both sides by 100.


7=e%5E%280.09%2At%29 Evaluate 700%2F100 to get 7.


ln%287%29=ln%28e%5E%280.09%2At%29%29 Take the natural log of both sides.


ln%287%29=0.09%2At%2Aln%28e%29 Pull down the exponent using the identity ln%28x%5Ey%29=y%2Aln%28x%29%29.


ln%287%29=0.09%2At%2A1 Evaluate the natural log of 'e' to get 1.


ln%287%29=0.09%2At Multiply and simplify.


1.94591014905531=0.09%2At Evaluate the natural log of 7 to get 1.94591014905531 (this value is approximate).


1.94591014905531%2F0.09=t Divide both sides by 0.09 to isolate 't'.


21.6212238783924=t Evaluate 1.94591014905531%2F0.09 to get 21.6212238783924.


t=21.6212238783924 Flip the equation.


t=22 Round to the nearest whole year.

So it will take about 22 years.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If 100 grows to 700, then A divided by P is 7.



Solve for

John

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