1. Complete 35 part a) on page 657 to write a DE using r=.05.
   
   
2. 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.
   
   
3. 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.
   
   
4. Apply Euler's method starting at (0,1) using 1 step with Δ t = .1
   
   
5. Reread the context of the problem and write an initial condition
   
   
6. 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.
   
   
7. Check your algebraic solution by plugging into the DE and showing it satisfies it.
   
   
8. At the initial condition, would Euler's method give an overestimate or underestimate? Use conceptual/visual reasoning rather than numerical computation to respond.