Question

Write a differential equation that models the given situation. the stated rate of change is with respect to time t. (use k for the proportionality constant.) the rate of change of the radius r of a tree trunk is inversely proportional to the radius.

Answer 1

To model the given situation, write the differential equation dr/dt = -k/r.

Step-by-step explanation:

To write a differential equation that models the situation described, we can use the proportionality constant k. The rate of change of the radius r of a tree trunk is inversely proportional to the radius. In mathematical terms, we can write this as:

dr/dt = -k/r

In this equation, dr/dt represents the rate of change of the radius with respect to time, k is the proportionality constant, and r is the radius of the tree trunk.