3) When modeling population growth of a new species (or virus), we often use the very important logistic curve P(t) =e, where A is some constant. 1+e-t [Note: You may have seen populations modeled exponentially as P(t) = Poe"t, or something similar. This model grows without bound, and so is not a very accurate in the long run. We are fancier now, and can use better models!] a. Graph P(t) on your calculator and sketch it here. Why might this model a population's growth well? b. We want to describe how fast it is growing at a given time, so we need to take the derivative [You may first want to find the derivative of e-]. Sketch the derivative. What is lim P'(t), and what does it mean?

3) When modeling population growth of a new species (or virus), we often use the very important logistic curve P(t) =e, where A is some constant. 1+e-t [Note: You may have seen populations modeled exponentially as P(t) = Poe"t, or something similar. This model grows without bound, and so is not a very accurate in the long run. We are fancier now, and can use better models!] a. Graph P(t) on your calculator and sketch it here. Why might this model a population's growth well? b. We want to describe how fast it is growing at a given time, so we need to take the derivative [You may first want to find the derivative of e-]. Sketch the derivative. What is lim P'(t), and what does it mean?

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

3) When modeling population growth of a new species (or virus), we often use the very important
logistic curve P(t) =-
, where A is some constant.
[Note: You may have seen populations modeled exponentially as P(t) = Poe"t, or
something similar. This model grows without bound, and so is not a very accurate in the long
run. We are fancier now, and can use better models!]
a. Graph P(t) on your calculator and sketch it here. Why might this model a population's
growth well?
b. We want to describe how fast it is growing at a given time, so we need to take the
derivative [You may first want to find the derivative of e-t]. Sketch the derivative. What
is lim P'(t), and what does it mean?

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Comment on the following statement: "The cost function for logistic regression trained with 100 examples is always non- negative."