Question

In math I have to use the equation A=Pe^rt to find the amount of time that it will take to double, and the amount of money after ten years. The initial investment is $10000 and the annual % rate is at 3.5% . I know that A= the accumulated amount P= the starting amount R= the annual rate and t= the amount of time. Can you show me how to slove this with step by step instructions? ( I already have the answers in the back of my book but that doesn't really help when you don't even know where to start!)Thanks!

Answer 1

the initial investment is not important
doubling time is doubling time

Answer 2

\[\large e^{.035t}=2\] sovle for \(t\)

Answer 3

doubling time is the time it takes \(e^{rt}\) to equal 2

Answer 4

So, the variables you are looking at are P=10,000 (since that is the initial investment), R=0.035 (interest turned into a decimal), and, for the last part, t=10 (years).

Now, first, to solve for doubling the investment, set A to 20,000 and solve for t using a natural logarithm. The property you will want to be using is: lnx=c and e^c=x.
20,000=(10,000)*e^(0.035t)
2=e^0.035t
Now, using the property mentioned above:
ln(2)=0.035t
ln(2)/0.035=t
t is approximately 19.804...
So, it will take that many years for the investment to double.

Now, to find the after ten years, you just solve this equation:
A=(10,000)*e^(0.035*10)
A=(10,000)*e^.35
A=14,190.675
Or, rounded to the nearest decimal point, $14,190.68

Answer 5

omit step one (always) and go right to \[2=e^{0.035t}\]

Answer 6

THANKS SO MUCH Hlares!!!! This totally just saved me and my math homework!!!!!