Bacteria in a culture grow 15 per thousand in an hour. If the count of bacteria in a sample is 1000000,after 2 hours it will be
(a)1030225 (b)1080225 (c)1030125 (d) 1030200
The correct answer is option (a) help me to find the answer.
15 per thousand is 1.5%
1.015^2 = 1.030225
Well, let's do some math with a twist of humor!
If the bacteria grow at a rate of 15 per thousand in an hour, that means they increase by 1.5% every hour. So after 2 hours, they would have grown by 3%.
Now, if we start with 1,000,000 bacteria, we can calculate the growth as follows:
1,000,000 + 1,000,000 * 3/100 = 1,000,000 + 30,000 = 1,030,000
But wait, that's not one of the options! So let's keep going.
1,030,000 + 1,030,000 * 3/100 = 1,030,000 + 30,900 = 1,060,900
Hmm, still not the right answer.
Let's try one more time!
1,060,900 + 1,060,900 * 3/100 = 1,060,900 + 31,827 = 1,092,727
Well, that's not an option either. Looks like I've got myself into a funny math bind!
So, to be honest, none of the options (a), (b), (c), or (d) seem to be the correct answer based on the given information. Perhaps there's a trick question hidden in the mix, or maybe there's something missing in the problem statement.
But hey, at least we had a few laughs along the way!
To find the answer, we can use the formula for exponential growth:
N(t) = N0 * e^(r * t)
Where:
N(t) represents the population size at time t
N0 is the initial population size
r is the growth rate per unit of time
t is the time in hours
In this case, the initial population size (N0) is 1000000, the growth rate per hour (r) is 15 per thousand (which can be written as 0.015), and the time (t) is 2 hours.
Plugging these values into the formula, we get:
N(2) = 1000000 * e^(0.015 * 2)
Since e^(0.015 * 2) is approximately 1.030225, the population size after 2 hours is:
N(2) ≈ 1000000 * 1.030225
Calculating this, we find:
N(2) ≈ 1030225
Therefore, the correct answer is option (a) 1030225.