The count of bacteria in a certain experiment was increasing at the rate of 2 per hour. Find the bacteria at the end of 2 hours if the count was initially 500000.
To find the count of bacteria at the end of 2 hours, you can use the formula for exponential growth:
N = N0 * e^(rt)
Where:
N = Final count of bacteria
N0 = Initial count of bacteria
e = Euler's number (approximately 2.71828)
r = Growth rate per unit of time
t = Time elapsed
In this case, the initial count is 500,000, the growth rate is 2 per hour, and the time elapsed is 2 hours.
Plugging these values into the formula, we have:
N = 500,000 * e^(2 * 2)
Calculating further:
N = 500,000 * e^4
To find the final count, we need to evaluate e^4 using a calculator or a mathematical software. The approximate value of e^4 is 54.59815 (rounded to five decimal places).
Therefore:
N ≈ 500,000 * 54.59815
N ≈ 27,299,075
So, at the end of 2 hours, the count of bacteria would be approximately 27,299,075.
Surely you mean either
2% per hour
or
doubling every 2 hours.
That would make the population either
500,000 * 1.02^2
or
500,000 * 2^1