Answer:
<em>P'(1.015)=4.93 grams</em>
Explanation:
<u>Instantaneous Rate Of Change
</u>
If one variable y is a function of another variable x, the rate of change can be measured by changing x by a small amount (dx) and computing the change in y (dy). The rate of change is

When dx tends to zero, we call it the instantaneous rate of change and is easily computed as the first derivative of y
Note: We'll be using the standart notation atan for the inverse tangent
We are given the relation between the mass of a colony of bacteria in grams P(t) and the time t in days

Let's find its first derivative, recalling that
![[atan(u)]'=\displaystyle \frac{u'}{1+u^2}](https://tex.z-dn.net/?f=%5Batan%28u%29%5D%27%3D%5Cdisplaystyle%20%5Cfrac%7Bu%27%7D%7B1%2Bu%5E2%7D)



We need to know the value of t, so we use the provided condition P=6 gr





We use this value in the derivative:

