+119 In just 5 weeks the population goes from 100 to 1000. What is the doubling time of this population? As in, how long does the population take to double?
i tried 1000=100(2)(t/5), where t is time in weeks
10=2(t/5)
log210=t/5
log(10)/log(2)=t/5
5*3.322=t
t=16.61
16.6 is quite a bit more than 5, which was the number of weeks it took to grow by 10x, so I knew that obviously wasn't correct. Can anyone help me figure out how this is solved or what formula is used?
+128460 We have this function :
P(t) = 100(e)kt
And when t = 5, we have that
1000 = 100(e)k5 divide both sides by 100
10 = e5k take the ln of both sides
ln 10 = ln e5k and we can write
ln 10 = 5k ln e { ln e = 1...so we can ignore this }
ln 10 = 5k divide both sides by 5
ln 10 / 5 = k
The function is
P(t) = 100(e) ln10 * t / 5
So.....we want to find the doubling time....and we have that
200 = 100(e)ln10 * t / 5 divide both sides by 100
2 = e ln 10 * t / 5 take the ln again
ln 2 = ln e ln 10 * / 5 amd we can write
ln 2 = [ (ln10) / 5 ] * t
5 ln 2 = ln 10 * t
5 ln 2 / ln 10 = t ≈ 1.5 weeks
