a. Use the formula for the general solution given in the text to sketch the solution of the logistic equation y' =y(1-y/10) with initial conditiony(0)=2. The standard form for our logistic equation isy'=ky(1-y/M). For our equation, what are k and M in this expression? What isy(6)?

y(6)=__________________

b. Let y' =ky(1-y/10) and y'(0)=2 and y(0)=5. What is y(4)?

y(4)= _____________________

c. A colony of bacteria is growing in a petri dish which has a maximum capacity of80mg. The mass of bacteria is increasing at a rate given by the logistic equation. Initially there is2mgof bacteria and the rate of increase is1mg per day. Write down the logistic equation satisfied by the mass,m.

m'=__________________

d. Species A doubles every1 hours and initially there are5 grams. Species B doubles every6 hours and initially there are10 grams. How long until the two species have the same mass? ______________________ hours

e. How many liters of water containing5grams of salt per liter must be combined withx liters of water which containsy grams (y is less than2) of salt per liter to yield a solution with2 grams of salt per liter.

Number of liters= ____________________________ (this should be an expression inx andy)