The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population of 1 million cells grew to 99 million. How large will the cell culture be after 25 hours

98 billion

Explanation:

1. Expression for rate of growth

Let Po = the original population

and P = the population at time t. Then

dP/dt = kP

dP/P = kdt

lnP = kt + C

At t = 0, lnPo = C

lnP = kt + lnPo

ln (P/Po) = kt

2. Value of k

ln (99 million/1 million) = k (10)

ln99 = 10k

k = ln99/10 = 4.595/10 = 0.4595/h

ln (P/Po) = 0.4595t

3. Population after 25 h

ln (P/Po) = 0.4595 * 25 = 11.49

P/Po = e^ (11.49) = 97 519

P = 97519No = 97 519 * 1 * 10^6 = 9.8 * 10^10 = 98 * 10^9

P = 98 billion.

In 25 h the population of the cell culture will be 98 billion.