find associated half life or doubling time.

[melody]

hi guys, i've been having trouble with this problem and i would really like some help.
find the associated half life or doubling time.
1800e^-0.025t
could anyone show me how to do it step by step. we were given the answer which is 40 ln(2), but i dont know how they got it.
thanks.

 

[tkhunny]

The little parameter in e's exponent is negative. This will be half life.

e^(-0.025t) = 1/2

Solve for t.

You thought it was tricky, didn't you?

 

[melody]

thanks for the reply but i am still a little confused.
after i tried to solve for t i didnt get the right answer which is 40 ln(2)
how do i solve for t ?

 

[lookagain]

thanks for the reply but i am still a little confused.
after i tried to solve for t i didnt get the right answer which is 40 ln(2)
how do i solve for t ?

melody,

there is a shortcut that I have memorized.

half-life \(\displaystyle =\)

\(\displaystyle \frac{ln(0.5)}{k} =\)

\(\displaystyle \frac{ln(2^{-1})}{k} =\)

\(\displaystyle \frac{-ln(2)}{k}\)

\(\displaystyle k = -0.025\) . . . by inspection of the exponent in the expression


half-life \(\displaystyle =\)

\(\displaystyle \frac{-ln(2)}{-0.025} =\)

\(\displaystyle 40ln(2) \approx 27.7\)

The half-life is about \(\displaystyle \ \ 27.7 \ years.\)

 

[tkhunny]

after i tried to solve for t i didnt get the right answer which is 40 ln(2)

If you are using a fancy calculator, you may have to rewrite your inputs a little. Rather than 0.025, use (1/40).

Please show what you DO get. Don't just tell us what you think you do NOT get.