When observations begin at t=​0, a cell culture has 1100 cells and continues to grow according to the function ​p(t)=1100+26t^4​, where p is the number of cells and t is measured in days.   a. Compute p′(t). What units are associated with the derivative and what does it​ measure? b. On the interval ​[0​,3​],

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A: Topic:- Derivative

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A: see 2nd step.

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A: On simplification, we get

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: