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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The number of bacteria after r hours in a controlled laboratory experiment is n = f(t).

(a) What is the meaning of the derivative f'(5)? What are its units?

(b) Suppose there is an unlimited amount of space and nutrients for the bacteria. Which do you think is larger, f'(5) or f'(10)? If the supply of nutrients is limited, would that affect your conclusion? Explain.

(a)

To determine

The meaning of f(5) and its units.

Explanation

Here f(t) is the number of bacteria after t hours in a controlled laboratory experiment.

Note that, the derivative f(x) is the instantaneous rate of change of the function f(x) with respect to x.

The derivative f(t) is rate of change of number of bacteria with respect to t hours in a controlled laboratory experiment.

Thus, f(5) is rate of change of number of bacteria with respect to 5 hours in a controlled laboratory experiment

(b)

To determine

To compare: The values f(5) or f(10) when bacteria has unlimited amount of space and nutrients and explain the conclusion when supply of nutrients is limited.

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