Fresh features from the #1 AI-enhanced learning platform.Try it free
Fresh features from the #1 AI-enhanced learning platformCrush your year with the magic of personalized studying.Try it free
Question

Let f(t) denote the amount of capital invested by a certain business firm at time t. The rate of change of invested capital, f(t)f^{\prime}(t), is sometimes called the rate of net investment. The management of the firm decides that the optimum level of investment should be C dollars and that, at any time, the rate of net investment should be proportional to the difference between C and the total capital invested. Construct a differential equation that describes this situation.

Solution

Verified
Answered 2 years ago
Answered 2 years ago
Step 1
1 of 2

If y=f(t)y=f(t) is the amount of capital invested by some business firm at time tt, then the rate of net investment is y=f(t)y'=f'(t). If the rate of net investment is supposed to be proportional to the difference between the optimum level of investment, CC, and the total invested capital, then we can write the differential equation as

y=k(Cy),\begin{aligned} \color{#4257b2}{y'=k(C-y)}, \end{aligned}

where kk is initially a positive constant.

Create an account to view solutions

Create an account to view solutions

Recommended textbook solutions

Thomas' Calculus 14th Edition by Christopher E Heil, Joel R. Hass, Maurice D. Weir

Thomas' Calculus

14th EditionISBN: 9780134438986Christopher E Heil, Joel R. Hass, Maurice D. Weir
10,144 solutions
Calculus and Its Applications 13th Edition by David C. Lay, David I. Schneider, Larry J. Goldstein, Nakhlé H. Asmar

Calculus and Its Applications

13th EditionISBN: 9780321848901David C. Lay, David I. Schneider, Larry J. Goldstein, Nakhlé H. Asmar
3,865 solutions
Calculus: Early Transcendentals 8th Edition by James Stewart

Calculus: Early Transcendentals

8th EditionISBN: 9781285741550 (3 more)James Stewart
11,084 solutions
Calculus: Early Transcendentals 9th Edition by Daniel K. Clegg, James Stewart, Saleem Watson

Calculus: Early Transcendentals

9th EditionISBN: 9781337613927Daniel K. Clegg, James Stewart, Saleem Watson
11,050 solutions

More related questions

1/4

1/7