Question

How do you solve `(1+(0.064/365))^(365t)=4`?

Answer 1

`t=346.58`

Explanation:

As `(1+0.004/365)^(365t)=4`, taking logs on both sides, we get

`365tlog(1+0.004/365)=log4`

or `365tlog(1+0.0000109589)=log4`

or `3655txx0.0000047593655=0.60206`

or `365t=0.60206/0.0000047593655=126500`

and `t=126500/365=346.58`

Answer 2

t~~500ln(2)~~346.57

Explanation:

As `(1+0.004/365)^(365t)=4`, taking lns on both sides, we get

`365t.ln(1+0.004/365)=ln4`

... as `0.004/365< <1:`

... #ln(1+0.004/365=0.004/365

So the expression turns into:

`365t(0.004/365)~~ln(4)`

`0.004t~~ln(4)`

t~~250ln(4)~~500ln(2)~~346.57