Answer:
The correct option is d) 12.75
Explanation:
Given,
The original price, P = $ 3.50,
Growth rate per year, r = 9.0% = 0.09,
So, the price after t years,
[tex]A = P(1+r)^t[/tex]
[tex]A=3.50(1+0.09)^t[/tex]
[tex]A=3.50(1.09)^t[/tex]
If A = 3P = 3(3.50) = 10.5,
[tex]10.5 = 3.50(1.09)^t[/tex]
[tex]3=(1.09)^t[/tex]
Taking log both sides,
[tex]\log 3 = \log(1.09)^t[/tex]
[tex]\log 3 = t\log (1.09)[/tex]
[tex]\implies t =\frac{\log 3}{\log 1.09}=12.7482\approx 12.75[/tex]
Hence, it will take 12.75 years for Ellis EPS to triple.
i.e. 'option d' is correct.
