Question 1160620: Suppose it takes 12 hours for a certain strain of bacteria to reproduce by dividing in half. If
35 bacteria are present to begin with, the total number present after
x days is
f(x)=35 * 4 ^ x
Fine the total number present after 1, 2, and 3 days.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! what this is saying is that the number of bacteria doubles every 12 hours.\
that means it is quadrupling every 24 hours, which is every day.
you start with 35 on day 0.
on day 1 you have 4 times as much as on day 0.
on day 2, you have 4 times as much as on day 1.
on day 3, you have 4 times as much as on day 2.
etc.....
the formula is:
f = p * 4 ^ x, where x is the number of days.
on day 0, you have 35 * 4 ^ 0 = 35.
on day 1, you have 35 * 4 ^ 1 = 140
on day 2, you have 35 * 4 ^ 2 = 560
on day 3, you have 35 * 4 ^ 3 = 2,240
the formula above assumes you start on day 0.
if you start on day 1, then the formula becomes:
f = p * 4 ^ (x - 1)
using this formula, you would get:
on day 1, you have 35 * 4 ^ 0 = 35
on day 2, you have 35 * 4 ^ 1 = 140
on day 3, you have 35 * 4 ^ 2 = 560
on day 4, you have 35 * 4 ^ 3 = 2,240
since your formula assumes 4 ^ x, then i believe the first day is day 0.
the function can be graphed as shon below.
|
|
|
