Unit 7: Differential Equations

Consider the differential equation [math] with initial condition [math].

Consider the differential equation [math].

A population of bacteria grows at rate proportional to its size. Initially there are 500 bacteria, and after 3 hours there are 1500.

A population [math] of fish in a lake satisfies the logistic equation [math] with [math].

Consider the differential equation [math].

Consider [math] with [math].

A cup of coffee at 190°F is placed in a room where the temperature is 70°F. The coffee cools according to Newton's law of cooling: [math].

Consider the differential equation [math] with [math].

Consider [math] with [math].

At each point [math] on a certain curve, the slope is given by [math]. The curve passes through [math].