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HOw many years will it take an investment of $35,000 to grow to$50,000 it it is invested at 4.75% compounded continuously

The answer is 7.51yr


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P = $35,000
A = $50,000
r = 4.75%
time, t = ?

A=P[1+ \frac{r}{100} ]^t\\ \\ \Rightarrow 50000=35000[1+ \frac{4.75}{100} ]^t\\ \\ \Rightarrow  \frac{50000}{35000} =[1+ 0.0475} ]^t\\ \\ \Rightarrow  \frac{10}{7} =[1.0475 ]^t\\ \\take\ log\ on\ both\ sides\\ \\ \Rightarrow log( \frac{10}{7}) =log([1.0475 ]^t)=t\ log(1.0475)\\ \\ \Rightarrow t= \frac{log( \frac{10}{7} )}{log(1.0475)} \\ \\ \Rightarrow t = 7.68\ years
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