SOLUTION: A certain bacterial infection has 110,000 organisms at 12:00pm. At 12:30 pm the population was 140,000. If this growth rate has been steady, when did the infection start?

Question 202641: A certain bacterial infection has 110,000 organisms at 12:00pm. At 12:30 pm the population was 140,000. If this growth rate has been steady, when did the infection start?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A certain bacterial infection has 110,000 organisms at 12:00pm. At 12:30 pm the population was 140,000. If this growth rate has been steady, when did the infection start?
--------------------------------
A(t) = Ao*(r)^t
---
r is the rate of growth
t is the time in minutes
---
140,000 = 110,000*r^(30)
14/11 = r^(30)
Take the log:
30*log(r) = log(14/11)
log(r) = [log(14/11)]/30
log(r) = 0.0034911784
r = 10^0.0034911784
r = 1.008071133 per minute
-------------------------------
1 = 110,000(1.008071133)^t
1.008071133)^t = 110,000^-1
t*log(1.998071133) = -log(110,000)
t = -16.7705 minutes
----------------------------
12:00 - 16.77 minutes is approximately 11:43 am
===================================================
Cheers,
Stan H.

RELATED QUESTIONS
A certain bacterial infection has 110,000 organisms at 12:00 p.m. on Wednesday at 12:30... (answered by stanbon)

A population numbers 12,000 organisms initially and decreases by 2% each year. Suppose (answered by greenestamps)

A medication is 75% effective against a bacterial infection. Find the probability that if (answered by stanbon)

MAT 145: Topics In Contemporary Math 20: Logistic Growth 2) A... (answered by ikleyn)

This is not a textbook question. A medication is 75% effective against a bacterial... (answered by stanbon)

In 1900, the population of Malthusian was 120,000. Since then, the population has... (answered by ankor@dixie-net.com,ikleyn)

A population numbers 19,000 organisms initially and decreases by 7% each year. Suppose (answered by ikleyn,math_tutor2020)

The following aged accounts receivable schedule was prepared for Dulax paints at the end... (answered by ikleyn)

A bacterial population has an exponential growth rate of 11.81% per hour. If there were... (answered by josgarithmetic,ikleyn)