Complete the table for the time t (in years) necessary for P dollars to triple when interest is compounded continuously at rate r. (Round your answers to two decimal places.)
R=2%
t=?
tried to plug in as A=Pe^rt since continiously
3=e^.02t ?
then take the ln of both sides?
(ln3/.02)=t?
3=e^rt
can't see the table, but you have correctly solved for t.
yes, about 55 years
10% doubles in about 7 years :)
ok this worked out great! thank you!
To complete the table for the time t necessary for P dollars to triple when interest is compounded continuously at rate r, you can use the formula for continuous compounding:
A = Pe^(rt)
Where A is the final amount, P is the initial principal, r is the interest rate (expressed as a decimal), and t is the time (in years).
In this case, you are given that the interest rate is 2% (or 0.02 expressed as a decimal), and you want to find the time it takes for the initial principal to triple (A = 3P).
Substituting the given values into the equation, you have:
3P = Pe^(0.02t)
Dividing both sides by P:
3 = e^(0.02t)
Taking the natural logarithm (ln) of both sides to solve for t:
ln(3) = 0.02t
Now, you can divide both sides by 0.02:
ln(3)/0.02 = t
To find the value of t, you can use a calculator or any software that can evaluate natural logarithms. By substituting ln(3)/0.02 into a calculator, you'll obtain the value of t rounded to two decimal places.
the table is just that
r 2% 4% 6% 8% 10% 12%
t ? ? ? ? ? ?
i will try that out then
Thank you