💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

In Exercise 9.1.15 we formulated a model for learning in the form of the differential equation$ \frac {dP}{dt} = k(M - P) $where $ P(t) $ measures the performance of someone learning a skill after a training time $ t, M $ is the maximum level of performance, and $ k $ is a positive constant. Solve this differential equation to find an expression for $ P(t). $ What is the limit of this expression?

$$\lim _{t \rightarrow \infty} P(t)=M-M \cdot 0=M$$

Calculus 2 / BC

Chapter 9

Differential Equations

Section 3

Separable Equations

Anaitl M.

March 10, 2021

A sphere with radius 1 m has temperature 11°C. It lies inside a concentric sphere with radius 2 m and temperature 19°C. The temperature at a distance r from the common center of the spheres satisfies the differential equation below. If we let S = dT/dr, t

Missouri State University

Campbell University

Baylor University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:24

Psychologists interested i…

10:15

05:18

Limited Growth Equation An…

02:41

05:54

Learning Curve A learning …

01:26

Suppose that a population …

00:50

Find the limits in Exercis…

01:08

06:00

The logistic growth model …

07:01

Another model for a growth…

we have the differential equation. The P on the tee he cost too key. Have minus p. It was separate variables. You have he p on a minus bi he caused to Kate. Time to DT integrating both sides. He's S d P on M minus p. He closed two key integral of tea. It is not negative in the natural law. A minus p you close to you, t plus C, which is a constant of integration when team courses there, he becomes the courses there. So it implies that my next natural look and becomes you close to see hands. I questioned them. Become negative. Natural law. M minus key. You cost you Katie minus a journal off. What? Right to buy Negative one gives me natural long off M minus key. You cost her actual off. M minus. Katie. Who? Pee line dance. Lean off. Am I this p call em? You close to Katie? So m minus p I m. You cost. He exponent, you go by the negative. Katie, It's negative, Katie. So I m dynasty in question. M times he explain our negative, Katie. So I make Peter subject P becomes cost. I m minus E em. Want to plant? Yes, but negative. Katie Cook tonight. Isn it solution to the French? I questions Now, if I limit this as TR pushes infinity gonna have limit us. T approaches Infinity. Oh, m minus and e minus. Katie today, which gives me m minus. Um, I want to play by zero. That is nasty. Approaches infinity. Yes, but minus K t approaches. Oh, sure. Limit to Europe, which is infinity off p as a function of time. It comes in Khost. Thank you.

Numerade Educator

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Psychologists interested in learning theory study learning curves. A learnin…

Limited Growth Equation Another differential equation thatmodels limited…

Learning Curve A learning curve is a graph of a function $P(t)$ that measure…

Suppose that a population grows according to the logistic equation $p^{\prim…

Find the limits in Exercises 21–36.$$\lim _{t \rightarrow 0} \frac{\…

The logistic growth model given in Formula (1) is equivalent to$$y e^{k …

Another model for a growth function for a limited population is given by the…