Answer :
Answer:
- 13
Step-by-step explanation:
Use formula for continuous interest:
- A = [tex]Pe^{rt}[/tex], where r- interest rate, t- time in years
If A = 3P, and r = 0.085 then the equation is:
- [tex]3P = Pe^{0.085t}[/tex]
- [tex]3 = e^{0.085t}[/tex]
- ln 3 = 0.085t
- 1.099 = 0.085t
- t = 1.099 / 0.085
- t = 12.9 ≈ 13 years
The formula for compounded continuously is A = Pe^rt where A if the final amount, P is the initial value, r is the rate and t is the length of time.
E is the constant for continuous interest.
Using the information from the problem $20 tripled would be 20x3 = $60
Now you have 60 = 20e^0.085(t)
We need to solve for t:
Divide both sides by 20:
e^0.085(t) =3
Apply the exponent rule:
0.085(t) = ln(3)
Solve for t:
T = ln(3)/0.085
T = 12.92 years. (Round off as needed)