precalculas
posted by katrina
the amount of bacteria in a petri dish increased by a percent change of 12% each hour over a period of 15 hours.
a. find the growth factor for 1 hour?
b. by what total percent did the bacteria change during this 15 hour time period.?
c. how long will it take for the bacteria to double?

drwls
a. 1.12
b. [(1.12)^15 1] x 100
The x 100 is for conversion %
c. about 6 hours, using the "rule of 72"
For the exact answer (t), solve
(1.12)^t = 2 
Reiny
your formula would be
Amount = a(1.12)^t , where 0 ≤ t ≤ 15
a) in 1 hour growth factor would be 1.12
b) Amount = a(1.12)^15 = 5.47a
percentage of growth = 5.47a/a = 5.47 or 547%
c)
2a = a(1.12)^t
2 = 1.12^t
log2 = log(1.12^t)
log2 = t log1.12
t = log2/log1.12 = 6.1 
drwls
I do not agree with Reiny's answer #2. They asked for the change, so 1 must be subtracted from 1.12^15
This would result in a 447% increase, to 547% of the initial value 
Reiny
drwls is correct, I should have subtracted to get the change.
(Can I blame it on the fact that I was only on my first cup of coffee ?)
Respond to this Question
Similar Questions

precal
A petri dish contains only two bacteria. The bacteria divide every half hour. How many bacteria will exist after 3 hours? 
Math
A culture of bacteria in a petri dish is doubling every hour. If there are 100 bacteria at time t=0, how many bacteria will there be in 12 hours? 
Math
How do I solve this if there is no equation to this 1. The population of the bacteria in a Petri dish increases by a factor of 10 every 10 hour. If there are initally 20 bacteria in the dish, how long will it take before the population … 
math
Bacteria is growing in a petri dish. Initially, there were 15,000 bacteria in the dish. It triples every 8 hours. Write the equation to represents this growth after t hours. 
Algebra 1
The initial number of bacteria in a Petri dish is 2,300 and grows at a rate of 3% per hour. Which best approximates the number of bacteria in the dish after 8 hours? 
calculus
a colony of bacteria living on a petri dish under optimal conditions doubles in size every ten minutes. At noon on a certain day, the Petri dish completely covered with bacteria. At what times (to the nearest hour, minute and second) … 
Algebra
At noon, Professor Simon has a petri dish with 10,000 cells of Bacteria A. In another petri dish, he has 33,000 cells of Bacteria B. Every hour, Bacteria A grows by 8%. Every hour Bacteria B cells die off, decreasing the number of … 
Math PLEASE HELP!!
At noon, Professor Simon has a petri dish with 10,000 cells of Bacteria A. In another petri dish, he has 33,000 cells of Bacteria B. Every hour, Bacteria A grows by 8%. Every hour Bacteria B cells die off, decreasing the number of … 
Math NEED HELP URGENT
At noon, Professor Simon has a petri dish with 10,000 cells of Bacteria A. In another petri dish, he has 33,000 cells of Bacteria B. Every hour, Bacteria A grows by 8%. Every hour Bacteria B cells die off, decreasing the number of … 
Honors Algebra
A biologist is researching a newly discovered species of bacteria. At time t=0 hours, she puts on hundred bacteria into a Petri dish. Six hours later, she measures 450 bacteria. Assuming exponential growth, what is the growth rate …