point Let N(t) measure the size of a population of bacteria after providing a nutrient for t > 0. N (1) = 4840 + 30000 100+1² Enter the first derivative N' (t) = Enter the critical number t = Is N(t) increasing or decreasing for f less than the critical number? Is N (1) increasing or decreasing for t greater than the critical number? What is the maximum size of the population?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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oint) Let N(t) measure the size of a population of bacteria after providing a nutrient for t > 0.
N(t) = 4840 +
30000
100+1²
Enter the first derivative N' (t) =
Enter the critical number t =
Is N (1) increasing or decreasing for t less than the critical number?
Is N (1) increasing or decreasing for t greater than the critical number?
What is the maximum size of the population?
Transcribed Image Text:oint) Let N(t) measure the size of a population of bacteria after providing a nutrient for t > 0. N(t) = 4840 + 30000 100+1² Enter the first derivative N' (t) = Enter the critical number t = Is N (1) increasing or decreasing for t less than the critical number? Is N (1) increasing or decreasing for t greater than the critical number? What is the maximum size of the population?
The trachea contracts during a cough to increase the velocity of air. The velocity can be modeled by
v = c(r-ro)r²,
where ro is the normal radius of the trachea, r is the radius during a cough and c is a negative constant.
If ro= 180, find the value of r that maximizes v on the domain [0, 180].
Transcribed Image Text:The trachea contracts during a cough to increase the velocity of air. The velocity can be modeled by v = c(r-ro)r², where ro is the normal radius of the trachea, r is the radius during a cough and c is a negative constant. If ro= 180, find the value of r that maximizes v on the domain [0, 180].
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