Respuesta :
Answer:
[tex] 300000= 100000 e^{0.12 t}[/tex]
We divide both sides by 100000 and we got:
[tex] 3 = e^{0.12 t}[/tex]
Now we can apply natural logs on both sides;
[tex] ln(3) = 0.12 t[/tex]
And then the value of t would be:
[tex] t = \frac{ln(3)}{0.12}= 9.16 years[/tex]
And rounded to the nearest tenth would be 9.2 years.
Step-by-step explanation:
For this case since we know that the interest is compounded continuously, then we can use the following formula:
[tex]A =P e^{rt}[/tex]
Where A is the future value, P the present value , r the rate of interest in fraction and t the number of years.
For this case we know that P = 100000 and r =0.12 we want to triplicate this amount and that means [tex] A= 300000[/tex] and we want to find the value for t.
[tex] 300000= 100000 e^{0.12 t}[/tex]
We divide both sides by 100000 and we got:
[tex] 3 = e^{0.12 t}[/tex]
Now we can apply natural logs on both sides;
[tex] ln(3) = 0.12 t[/tex]
And then the value of t would be:
[tex] t = \frac{ln(3)}{0.12}= 9.16 years[/tex]
And rounded to the nearest tenth would be 9.2 years.
