A bacteria culture starts with 420 bacteria and grows at a rate proportional to its size. After 6 hours there will be 2520 bacteria.
Express the population after t hours as a function of t .
Express the population after t hours as a function of t .
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For A to be proportional to B, means that there exists some K, such that A=KB.
Thus, the Growth = K*420. Now we need to relate the K to a rate and time.
If the bacteria were to double every hour then we would have Growth = 420* (2^t), where if t=0 (the zero hour) we would have Growth = 420, which is what the bacteria starts at. But the bacteria does not double every hour, we actually don't know the rate of growth.
We are given that after 6 hours there is a growth of 2520 bacteria. So lets use that info (Let r = the unknown bacteria growth rate):
2520 = 420*r^6
6 = r^6
r = 6^(1/6)
So now that we know the rate of growth we can write the growth of the bacteria as a function of time:
G(t) = 420*6^(t/6)
Thus, the Growth = K*420. Now we need to relate the K to a rate and time.
If the bacteria were to double every hour then we would have Growth = 420* (2^t), where if t=0 (the zero hour) we would have Growth = 420, which is what the bacteria starts at. But the bacteria does not double every hour, we actually don't know the rate of growth.
We are given that after 6 hours there is a growth of 2520 bacteria. So lets use that info (Let r = the unknown bacteria growth rate):
2520 = 420*r^6
6 = r^6
r = 6^(1/6)
So now that we know the rate of growth we can write the growth of the bacteria as a function of time:
G(t) = 420*6^(t/6)