SOLUTION: The doubling period of a bacterial population is 20 minutes. At time t=90 minutes, the bacterial population was 50000. What was the initial population at time t=0 ?

Algebra ->  Customizable Word Problem Solvers  -> Unit conversion -> SOLUTION: The doubling period of a bacterial population is 20 minutes. At time t=90 minutes, the bacterial population was 50000. What was the initial population at time t=0 ?       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 993293: The doubling period of a bacterial population is 20 minutes. At time t=90 minutes, the bacterial population was 50000.
What was the initial population at time t=0 ?
Find the size of the bacterial population after 3 hours
*formula: p(t)=a(b)^t
**Note:b=1+r
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
p=a%2Ab%5Et and you have some information for doubling time. Twenty minutes is 1%2F3 hour. Try to use just that much and see what you can find.

Try taking a as the initial population when t=0.
system%28t=1%2F3%2Cp=2%2Ca=1%29,
.
2=1%2Ab%5E%281%2F3%29
b=root%283%2C2%29, or b=1.26 approximately.
The model might work as p=a%2A%281.26%29%5Et.

The next part of the description is the given point (1.5, 50000), and you want to know a, or value of p when t=0 instead of t=1.5.
a%2A%281.26%29%5E%283%2F2%29=50000

a=50000%2F%281.26%29%5E%283%2F2%29
and for convenience, recall where the "1.26" came from:
a=50000%2F%28root%283%2C2%29%29%5E%283%2F2%29
...the rendering does not look properly aligned but that is an equation, formula for a = fifty thousand over (cube root of two) to the three-halves power...
a=50000%2F%282%5E%281%2F3%29%29%5E%283%2F2%29
a=50000%2F%282%5E%28%281%2F3%29%283%2F2%29%29%29
a=50000%2F%282%5E%281%2F2%29%29
highlight%28a=50000%2Fsqrt%282%29%29, simple radical form, although denominator is not rationalized.

This would be about highlight%28a=35400%29.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
The doubling period of a bacterial population is 20 minutes. At time t=90 minutes, the bacterial population was 50000.
What was the initial population at time t=0 ?
Find the size of the bacterial population after 3 hours
*formula: p(t)=a(b)^t
**Note:b=1+r
r, or growth rate = .035264924 ≈ 3.526%, per minute

Initial population at time = 0 minutes: 2,209.708691 ≈ highlight_green%282210%29

Population at time = 3 hours (180 minutes): 1,131,370.8499 ≈ highlight_green%281131371%29