Using the equation of continuous compounding, the correct options are: A, D, E and F, and that it will take 18.31 years for the amount to triple.
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The amount of money, in continuous compounding, after t years, is given by:
[tex]A(t) = A(0)e^{kt}[/tex]
In which
- A(0) is the initial amount.
- k is the interest rate.
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- Interest rate of 6% means that [tex]k = 0.06[/tex], and thus:
[tex]A(t) = A(0)e^{0.06t}[/tex]
- The amount will triple when:
[tex]A(t) = 3A(0)[/tex]
Thus:
[tex]A(t) = A(0)e^{0.06t}[/tex]
[tex]3A(0) = A(0)e^{0.06t}[/tex]
[tex]3 = e^{0.06t}[/tex]
Which is option F. Additionally, options A, D and E can be simplified to this equation, thus, they are the correct options.
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- Solving for t, we find the time needed, thus:
[tex]e^{0.06t} = 3[/tex]
[tex]\ln{e^{0.06t}} = \ln{3}[/tex]
[tex]0.06t = \ln{3}[/tex]
[tex]t = \frac{\ln{3}}{0.06}[/tex]
[tex]t = 18.31[/tex]
It will take 18.31 years for the amount to triple.
A similar problem, is given at https://brainly.com/question/15953707
