How do you solve ${(1 + (\frac{0.064}{365}))}^{365 t} = 4$ $(1+(0.064/365))^(365t)=4$ ?

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Answer 1 · 2017-10-16T13:17:24

$t = 346.58$ $t=346.58$

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

$365 t log (1 + \frac{0.004}{365}) = log 4$ $365tlog(1+0.004/365)=log4$

or $365 t log (1 + 0.0000109589) = log 4$ $365tlog(1+0.0000109589)=log4$

or $3655 t \times 0.0000047593655 = 0.60206$ $3655txx0.0000047593655=0.60206$

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

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

Answer 2 · 2017-10-27T18:28:03

t~~500ln(2)~~346.57

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

$365 t . ln (1 + \frac{0.004}{365}) = ln 4$ $365t.ln(1+0.004/365)=ln4$

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

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

So the expression turns into:

$365 t (\frac{0.004}{365}) \approx ln (4)$ $365t(0.004/365)~~ln(4)$

$0.004 t \approx ln (4)$ $0.004t~~ln(4)$

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

How do you solve (1+(0.064/365))^(365t)=4(1+(0.064365))365t=4(1+(0.064/365))^(365t)=4?