A type of bacteria doubles in number every 12 hours. After 2 days, there are 48 bacteria. How many bacteria were there at the beginning of the first day.
2 days is 4 doublings, or 16 times the original amount.
So, there were 3 to begin.
Thank you Steve.
But I want to know how to show it.
Thanks once again
every 12 hours, the population doubles. So, if it starts out as p, then after t hours, we have
p*2^(t/12)
for t=48, then,
p*2^(48/12) = 48
p*2^4 = 48
16p = 48
p = 3
To solve this problem, we can set up an exponential growth equation to represent the doubling of bacteria every 12 hours.
Let's denote the initial number of bacteria as 'x'. After 12 hours, the number of bacteria will be 2x (doubling). After another 12 hours (24 hours in total), it will be 4x (doubling again).
Now, after 2 days, which is equivalent to 48 hours, we need to solve for 'x' in the equation 4x = 48.
To solve for 'x', we can divide both sides of the equation by 4:
4x/4 = 48/4
x = 12
Hence, at the beginning of the first day, there were 12 bacteria.