- Complete 35 part a) on page 657 to
**write a DE** using r=.05.

- Next use the DE to sketch a
**slope field** at the 4 points (0,0), (0,1), (1,0), (1,1), where *t* is on the *x*-axis.

- Are there any
**equilibrium solutions** where the differential
equation is always 0? If so are they stable or unstable? Use the DE, your slope field, and the
context of the real-life situation to respond.

- Apply
**Euler's method** starting at (0,1) using 1 step with Δ
*t* = .1

- Reread the context of the problem and write an
**initial condition**

- Complete 35 part b) on page 657 and show work for the
**algebraic
solution**, including the
algebra to solve for *M* as well as how you applied the initial condition.

**Check your algebraic solution** by plugging into the DE and
showing it satisfies it.

- At the initial condition, would
**Euler's method** give an overestimate or underestimate?
Use conceptual/visual reasoning rather than numerical computation to respond.