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

Oct 16, 2017

$t = 346.58$

#### Explanation:

As ${\left(1 + \frac{0.004}{365}\right)}^{365 t} = 4$, taking logs on both sides, we get

$365 t \log \left(1 + \frac{0.004}{365}\right) = \log 4$

or $365 t \log \left(1 + 0.0000109589\right) = \log 4$

or $3655 t \times 0.0000047593655 = 0.60206$

or $365 t = \frac{0.60206}{0.0000047593655} = 126500$

and $t = \frac{126500}{365} = 346.58$

Oct 27, 2017

t~~500ln(2)~~346.57

#### Explanation:

As ${\left(1 + \frac{0.004}{365}\right)}^{365 t} = 4$, taking lns on both sides, we get

$365 t . \ln \left(1 + \frac{0.004}{365}\right) = \ln 4$

... as $\frac{0.004}{365} < < 1 :$

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

So the expression turns into:

$365 t \left(\frac{0.004}{365}\right) \approx \ln \left(4\right)$

$0.004 t \approx \ln \left(4\right)$

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