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Slope Fields

13. Intro to Differential Equations / Slope Fields / Problem 5

Problem 5

Sketch a direction field for the following differential equation and the solution curve corresponding to the given initial condition. Assume $t is greater than or equal to 0$ and $P is greater than or equal to 0$ .
$P^{'} (t) = 0.02 P (1 - \frac{P}{1000})$ , $P of 0 equals 200$

A

Direction field with colored slope lines and a blue solution curve starting at 200, approaching 1000 as time increases.

B

Direction field with colored slope segments and a blue solution curve starting at 200, leveling off near 600 as t increases.

C

Direction field plot with slope lines and a blue solution curve starting at 200, approaching 1000 as t increases.

D

Direction field with colored slope segments and a blue solution curve starting at 200, approaching 1000 as t increases.