Question 978605: A certain bacteria population is known to doubles every 90 minutes. Suppose that there are initially 160 bacteria.
What is the size of the population after t hours?
please help, ive sent this a few times and still have no response and or a legit answer. I've tried multiple times and im unsure what to do with the 90... so i convert that to hours? in the exponent?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! P=Po{1+r}^1.5 ;;time is in hours. You could use minutes, but hours is what is desired and it makes the exponent smaller.
P/Po=2 (doubling); Po=160
2=(1+r)^1.5
ln2 =1.5 * ln (1+r)
0.693=1.5 *ln (1+r); divide by 1.5 both sides
0.462=ln (1+r); raise both to e power
1.5872=(1+r)
r=0.5872
After t hours, the population, P=160 (1.5872)^t
Check. After 3 hours, the population has doubled twice or increased 4 times.
P=160 (1+r)^3=160(1.5872)^3
1.5872^3= 3.998, or 4 by rounding.
P=160*4=640. That is quadrupling.
After 24 hours, the population has increased by 1440/90 or 16 doubling times or by a factor of 2^16
2^16=65536
P=160(1+ 0.5872)^24
1.5872^24=65537, which is by rounding, very close to 65536, and that is 2^16
P=160*65536=10,485,760
|
|
|
