A calf that weighs 60 pounds at birth gains weight at the rate dw/dt = k(1200 - w)
1 answer:
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.
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