Question 1149204
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If interest is compounded continuously at the rate of 3% per year, approximate the number of years 
it will take an initial deposit of $7000 to grow to $27,000. (Round your answer to one decimal place.)
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        The solution and the answer in the post by @addingup to both problems are incorrect.

        It is because his starting setup equation is incorrect, which is a conceptual/strategic error.


        I came to bring a correct solution.



<pre>
The setup equation for this continuously compounded account is

    27000 = {{{7000*e^(0.03*t)}}},    <<<---===  It is a standard translation
                                           for a continuously compound account

where 't' is the time in years.


Divide both sides by 7000 to get

    {{{27000/7000}}} = {{{e^(0.03*t)}}}.


Take natural logarithm of both sides

    {{{27000/7000}}} = 0.03*t.


Express 't' and calculate

    t = {{{(1/0.03)*ln(27000/7000)}}} = 44.9976 years.


It is reasonable to round it to the closest integer, which is 45 years.


<U>ANSWER</U>.  45 years.
</pre>

Solved correctly, so you can learn/teach safely from my post.


Ignore the post by @addingup, since it is wrong solution and wrong teaching.