The population of a culture of bacteria has a growth rate given by p(t)=210/(t+1)^r

bacteria per hour, for t0,

where r>1 is a real number. The increase in the population over the time interval [0,t] is given by

0t p(s)ds.

(Note that the growth rate decreases in time, reflecting the competition for food and space.) Complete steps (e) below.

Using the population model with r=3,

what is the increase in the population over the time interval 0t6?

The increase in the population over the given interval is approximately 102 bacteria.

Work with the population model using r=3

(part (b)) and find the increase in population over the time interval [0,T] for any T>0.

If the culture is allowed to grow indefinitely (T),

does the bacteria population increase without bound? Or does it approach a finite limit?

The bacteria population approaches a finite limit at ?