Dw/dt = k(1200 - w)
dw/(1200 - w) = kdt
-ln(1200 - w) = kt + c
When t = 0, w = 60
-ln(1200 - 60) = c
c = -ln(1140)
a.) For k = 0.8: -ln(1200 - w) = 0.8t - ln(1140)
t = [ln(1140) - ln(1200 - w)]/0.8
For k = 0.9:
t = [ln(1140) - ln(1200 - w)]/0.9
For k = 1:
t = [ln(1140) - ln(1200 - w)]
b.) For k = 0.8
t = [ln(1140) - ln(1200 - 800)]/0.8 = [ln(1140) - ln(400)]/0.8 = 1.3 years
For k = 0.9
t = [ln(1140) - ln(400)]/0.9 = 1.16 years
For k = 1
t = [ln(1140) - ln(400)] = 1.05 years
c.) For maximum weight,
dw/dt = 0
k(1200 - w) = 0
1200 - w = 0
w = 1200
Therefore, the maximum weight for each of the model is 1200 pounds.
