Help with log problem
I am not sure what to use for this problem, I think it is a log is there any formula I could use to solve this ? Any help appreciated, I am studying problems from old exams to practicing for my exam !!
A ship is leaking oil, it doubles the area it covers every 7 days. If the initial leakage area is 15 square metres how long would it take to cover 25000 metres squared.
I had typed out a nice explanation but firefox had an error so here it goes again. I have learned to copy and temporarily save as I type now. :(
It seems to be an exponential function since it doubles every week, . So
Dividing by 15, we get
Taking the log base two of each side, we get
So or if needed in days, multiply by 7, of course.
After 7 days the covered area is 2 x 15 m^2
Originally Posted by gregorio
After 14 days the covered area is 4 x 15 m^2
After 21 days the covered area is 2^3 x 15 m^2
After 7N days the covered area is 2^N x 15 m^2
If after 7N days the area covered is 25000 m^2, we have:
25000 = 2^N x 15.
Now take logs (any base it does not matter):
log(25000) = N log(2) + log(15),
N = [log(25000) - log(15)]/log(2) = log(5000/3)/log(2) ~=10.7
So the oil covers the required area after about 7 x 10.7 ~= 75 days