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?
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
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
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
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 ?)
To answer these questions, we need to understand how to calculate a growth factor, calculate the total percent change over a given period, and determine the time it takes for the bacteria to double.
a. To find the growth factor for 1 hour, we first convert the percent change to a decimal by dividing 12% by 100: 12% ÷ 100 = 0.12. Then we add 1 to this decimal value: 0.12 + 1 = 1.12. Therefore, the growth factor for 1 hour is 1.12.
b. To calculate the total percent change over 15 hours, we need to multiply the growth factor for 1 hour repeatedly for 15 times. Since the growth factor for 1 hour is 1.12, we can raise it to the power of 15: 1.12^15. Evaluating this expression will give us the total growth factor over 15 hours.
c. To determine how long it will take for the bacteria to double, we need to find the number of times the growth factor needs to be multiplied until it reaches 2. We can use the formula:
Doubling time (in hours) = log(2) / log(growth factor)
Here, "log" denotes the logarithm function with base 10, and the growth factor is the same as the one calculated in part (a).
By following these steps, we can now proceed to calculate the answers to the questions.