Question

Mark monitors the growth of a colony of bacteria in his biology lab. He begins with a colony of 100 bacteria. After 24 hours, the colony has grown to 305

bacteria. After 24 more hours, the colony consists of 897 bacteria. What is a reasonable estimate of how many bacteria he can expect to count in the colony

when he returns 24 hours later?

Answer 1

After next 24 hours, bacterial population would be
`1433`

Explanation:

The initial bacterial count at time = 0 was
`100`

At
`= 24` hours, the bacterial count increased up to
`305`

At
`= 48` hours, the bacterial count increased up to
`897`

As we know that

`P = P_0 * e^(rt)`

The growth rate of bacterial population is equal to

`r = (log(P)/(P_0) )/(t)`

Substituting the above values we get -

`r = (log(897)/(305) )/(24)\\r = 0. 0195`

Count of bacteria after next 24 hours

`P = 897 * e^{ 0.0195 * 24)\\P = 1433`