suppose that N(t), the number of bacteria is a culture at time t is given by N(t) =...

Question:

suppose that N(t), the number of bacteria is a culture at time t is given by N(t) = {eq}25+te^{-\frac{t}{20}} {/eq}, where N is measured in millions of bacteria and t is in hours.

(a) at what time during the interval {eq}[0,100] {/eq} is the number of bacteria the smallest? what is the minimum number?

(b) at what time during the interval {eq}[0,100] {/eq}is the number of bacteria the largest? what is the maximum number?

(c) at what time during the interval {eq}[0,100] {/eq} is the number of bacteria a minimum ?

Minima and Maxima:

We will first check the minimum and the maximum that is by differentiating the function and then putting it equal to 0 and then we will check for the value of the function at the end points also.

Answer and Explanation:

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To find the minimum or maximum bacteria let us first differentiate the equation:

{eq}N=25+te^{\frac{-t}{20}} {/eq}

Now differentiating it we get:

...

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Minimum Values: Definition & Concept

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Chapter 18 / Lesson 16
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The minimum value of a quadratic function is the low point at which the function graph has its vertex. This lesson will define minimum values and give some example problems for finding those values. A quiz will complete the lesson.


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