50 points! I understand A. and B. but I would really appreciate help with C.

Step-by-step explanation:

So, the function, P(t), represents the number of cells after t hours.

This means that the derivative, P'(t), represents the instantaneous rate of change (in cells per hour) at a certain point t.

C)

So, we are given that the quadratic curve of the trend is the function:

To find the instanteous rate of growth at t=5 hours, we must first differentiate the function. So, differentiate with respect to t:

Expand:

Move the constant to the front using the constant multiple rule. The derivative of a constant is 0. So:

Differentiate. Use the power rule:

Simplify:

So, to find the instantaneous rate of growth at t=5, substitute 5 into our differentiated function:

Multiply:

Subtract:

This tells us that at exactly t=5, the rate of growth is 51.72 cells per hour.

And we're done!

idc

step-by-step explanation:

idk

step-by-step explanation: