cells in a culture are doubling every 14 hours. there were 1000 cells initially.
A) create an equation relating the number of cells (N) that will be doubled, to an exponent where 'h' represents the doubling time in hours and 't' represnts the time since the cels started at 1000
N= ??
B) Approximately how many cells will there be after 2 days?
Let the doubling time, or h = t/14, where t = number of hours elapsed. Therefore we have:
N =1,000 x 2^h. So, in 2 days or 48 hours we have:
h =48/14 =3 3/7 - number of doublings:
N = 1,000 x 2^(24/7)
N = 1,000 x 10.76720.....
N =~10,767 - expected number of cells in 2 days or 48 hours.
+245 A.)
Think of this problem as an interest problem. After a certain amount of time, your money (cells) will double.
The standard equation for simple compounding interest is y = P(R)^x
where
P is the principal/ initial amount
R is the rate at which your principle will increase
x is the time interval (seconds, days, year, etc.)
y is the final amount after x time
Knowing that we can make an equation
N= 1000(2)^(h)
where h is (t/14)
t is in hours so every fourteen hours the expression h increases by 1 and so the equation N doubles.
B.)
There are 24 hours in a day so in 2 days that is 48 hours
h will then be 48/14
plug this into the equation and you get
N= 1000(2)^(48/14) = 10767 cells (rounding down because you can't have a portion of a cell)
