The mass of a colony of bacteria, in grams, is modeled by the function p given by p(t)=2+5tan^−1.(t/2), where t is measured in days. what is the instantaneous rate of change of the mass of the colony, in grams per day, at the moment the colony reaches a mass of 6 grams?

1.21 g/day

Step-by-step explanation:

We are given that

The mass of a colony of bacteria (in (grams) is given by

Where t=Time(in days)

Differentiate w.r.t t

By using the formula

We are given P(t)=6

Substitute the value

Substitute the value of t

We know that

Using the formula

By using

g/day

Hence,the instantaneous rate of change of the mass of the colony=1.21g/day

The instantaneous rate of change of mass can be calculated as    where is rate of change with small amount .

Thus, the instantaneous rate of change of the mass of the colony is .

Given:

The mass of a colony of bacteria, in grams, is modeled by the function given by

,

where is measured in days.

Differentiating the function with respect to .

Now,

Then,

Substituting the value of in above equation,

Hence, the instantaneous rate of change of the mass of the colony is

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