Chapter 7.5, Problem 44E

To determine

To find which of the following differential equations would produce the slope field .

Answer to Problem 44E

Option B is correct.

Explanation of Solution

Given information: given option.

  $\begin{array}{l}\left(A\right)\frac{dy}{dx}=0.01x\left(120-x\right)\\ \left(B\right)\frac{dy}{dx}=0.01y\left(120-y\right)\\ \left(c\right)\frac{dy}{dx}=0.01y\left(100-x\right)\\ \left(D\right)\frac{dy}{dx}=\frac{120}{1+60e^{-1.2x}}\\ \left(E\right)\frac{dy}{dx}=\frac{120}{1+60e^{-1.2y}}\end{array}$

Given graph.

  

The shape of the slope field looks like a logistic population curve. Only option (B) has the proper formulation.

Hence, option B is correct.