# Math Help - exponential functions

1. ## exponential functions

A man jumps from above - his speed of descent is given by V = 50(1-2^-0.2t) m/s where t is the time in seconds. Find the time taken for his speed to reach 40 m/s.

I know to set the equation to:

40 = 50(1 - 2^-0.2t)

but i can't seem to carry it out from there..because i can't take the log of both sides when the numbers are negative.

2. rearrange it to get the $2^{-0.2t}$ by itself.. eg:

$40 = 50(1-2^{-0.2t})$
=>
$40 = 50 - 50*2^{-0.2t}$
=>
$-10 = -50*2^{-0.2t}$
=>
$1/5 = 2^{-0.2t}$

then take logs of both side and continue. you should get something like $t = 5 \frac{\log{5}}{\log{2}}$