A culture contains 12,000 bacteria. After an hour the count is 25,000. Find the number of bacteria after 3 hours.
To find the number of bacteria after 3 hours, we need to determine the growth rate per hour.
First, let's find the growth factor per hour, which is calculated by dividing the final count by the initial count:
Growth factor = Final count / Initial count = 25,000 / 12,000 = 2.0833 (rounded to four decimal places)
Next, we can find the growth factor after 3 hours by raising the growth factor per hour to the power of the number of hours:
Growth factor after 3 hours = Growth factor per hour ^ Number of hours = 2.0833 ^ 3 = 9.26 (rounded to two decimal places)
Finally, we can calculate the number of bacteria after 3 hours by multiplying the initial count by the growth factor after 3 hours:
Number of bacteria after 3 hours = Initial count * Growth factor after 3 hours = 12,000 * 9.26 = 111,120 (rounded to the nearest whole number)
Therefore, the number of bacteria after 3 hours is approximately 111,120.
To find the number of bacteria after 3 hours, let's first determine the rate at which the bacteria are increasing per hour.
In one hour, the number of bacteria increased from 12,000 to 25,000, which means there was an increase of 25,000 - 12,000 = 13,000 bacteria in one hour.
To calculate the number of bacteria after 3 hours, we multiply the increase per hour by the number of hours:
13,000 bacteria/hour * 3 hours = 39,000 bacteria
Therefore, the number of bacteria after 3 hours would be 39,000.
let's assume the growth of bacteria is "almost" continuous
so number = initial value e^(kt) where k is a constant
so 12000 e^(1k) = 25000
e^k = 2.0833333...
k = ln 2.083333.. =.733969
number after 3 hrs = 12000 e^(3(.733969)) = 108506.9 or
109,000 to the nearest thousand