1290=160e(in2/2)(t)?
hot do i caculate t?

Question

1290=160e(in2/2)(t)?
hot do i caculate t?

hartnn · Answer

what is 'in' ??
or is your question,
$\huge 1290=160e^{\ln 2/2}$

anonymous · Answer

yes thats right.

phi · Answer

where does the t go ?

hartnn · Answer

okk...then use  $\huge x^{b/2}= \sqrt {x^b}$
and $\huge e^{ln x}=x $

hartnn · Answer

oh, yeah, what about t ? :P

anonymous · Answer

t is also exponent next In2/2

anonymous · Answer

and i have to solve for t

phi · Answer

the first step is divide both sides by 160

hartnn · Answer

like $\huge 1290=160e^{t\ln 2/2}$
?

anonymous · Answer

no t in the end

hartnn · Answer

anyways do what @phi  said...

anonymous · Answer

8.0625?

phi · Answer

do you mean:
$$ 1290= 160 e^{\frac{\ln 2}{2} t } $$
that is the same as
$$ 1290= 160 e^{\frac{t \ln 2}{2} } $$

anonymous · Answer

oh i didnt know that! cool :)

hartnn · Answer

next step is to take natural log on both sides...

anonymous · Answer

how do i do that

phi · Answer

I would do
$$ \frac{1290}{160} = e^{t \frac{\ln 2}{2}} $$
then write ln on both sides:
$$\ln\left( \frac{1290}{160}\right) = \ln\left(e^{t \frac{\ln 2}{2}} \right)$$

phi · Answer

ln "undoes" the e to the exponent.  it brings down the exponent of e

phi · Answer

in other words  
$$\ln(e^x)= x $$

phi · Answer

no matter how complicated  "x" is

phi · Answer

the left side is some number
the right side is
$$ \frac{\ln 2}{2} t $$
solve for t by multiplying both sides by 2/ln 2

anonymous · Answer

Ok, ! i got 2.794

anonymous · Answer

mmm... i entered the answer on online homework and it says it was wrong

phi · Answer

Did you check your answer ?  I did not get 2.794

anonymous · Answer

i keep geting 2.794249

phi · Answer

so far we have
$$ \ln\left( \frac{1290}{160}\right) = t \frac{\ln 2}{2} $$

anonymous · Answer

yes.

phi · Answer

solve for t to get
$$t=  \frac{2}{\ln 2} \cdot \ln\left( \frac{1290}{160}\right)  $$

phi · Answer

what steps are you taking ?

anonymous · Answer

oh  i didnt know do In (1290/160) I just caculated without In

phi · Answer

go back and look how we did it.  We had to take the log of both sides.

anonymous · Answer

i mean i didnt do. haha

anonymous · Answer

I got 6.0224!

phi · Answer

yes, that looks good.  If you use that number in the original equation it will work out.

anonymous · Answer

Thank you very much :)
so excited when I got the number! 
you are the star!

phi · Answer

thank you