5. Hopefully your answer to the previous question included the word "slope." A nice way to visualize solutions to differential equations is with a slope field. For any value of t and M, we plug into...

We know that M(0)=10 and that M'(0) = 23

If we move in that direction from t=0 to t=1, by what amount will M change?

0.0 1.0 2.0 3.0 4.0 5.0 6.0 ノ///ニ 20 "/>
Extracted text: 5. Hopefully your answer to the previous question included the word "slope." A nice way to visualize solutions to differential equations is with a slope field. For any value of t and M, we plug into right-hand side of the differential equation to get the slope, dM/dt, and indicate the slope at that point in the t-M plane by a short line segment as shown in the figure below. In this plot, r =1 and K = 100, and the horizontal axis is t and vertical is M. M 120 100 80 60 40 MlO)=10-> 0.0 1.0 2.0 3.0 4.0 5.0 6.0 ノ///ニ 20


Extracted text: In this activity we will look at how we can approximate solutions to differential equations without actually solving them. We will consider a model for a tumor growth known as the Gompertz growth function. Let M(t) > 0 be the mass of a tumor at timet2 0. The relevant differential equation is dM -rM In K dt