Question

A calf that weighs 60 pounds at birth gains weight at the rate dw/dt = k(1200 - w)
Calculus question please help!

Answer 1

Weight Gain A calf that weighs 60 pounds at birth gains
weight at the rate
dw􏰂k􏰋1200􏰆w􏰌 dt
where w is weight in pounds and t is time in years. Solve the differential equation.
(a) Use a computer algebra system to solve the differential equation for k 􏰂 0.8, 0.9, and 1. Graph the three solutions.
(b) If the animal is sold when its weight reaches 800 pounds, find the time of sale for each of the models in part (a).
(c) What is the maximum weight of the animal for each of the models?

Answer 2

\[\frac{dw}{dt} = k(1200-w)\]
\[\int\limits \frac{dw}{1200 - w} = k \int\limits dt\]
\[-\ln (1200-w) = kt + C\]
\[1200 - w = e^{-kt +C}\]
\[w = 1200 - e^{-kt + C}\]
plug in initial value, t=0, w = 60 to find C
\[C = \ln (1140)\]
\[w = 1200 - 1140e^{-kt}\]
plug in the different values for k, set w = 800, and solve for t
\[t = \frac{\ln (\frac{1200-w}{1140})}{-k}\]
max weight is 1200 because at that weight dw/dt = 0 and dw/dt is negative for w>1200

Answer 3

Thank you so much! :D

Answer 4

your welcome