Estimate the amount of solid 1 second later

Question

Let f(t) be the weight (in grams) of a solid sitting in a beaker of water after t minutes have elapsed. Suppose that the solid dissolves in such a way that the rate of change (in grams/minute) of the weight of the solid at any time t can be determined from the weight using the forumula:

 

fprime(t)=-5f(t)(5+f(t))

 

If there is 6 grams of solid at time t=2 estimate the amount of solid 1 second later.

Answer 1

It is given that f(2) = 6 grams

 

The rate of change of weight at time t= 2 will be

 

fprime(2) =-5*f(2)*(5+f(2)) = -5*6*(5+6) = -330 gms / minute = -0.727 pounds / minute = -0.012 pounds / sec

 

Therefore the weight of the ice at time = 2 is decreasing by 0.012 pounds / sec

 

Its weight after 1 second will be  6 - 0.012 = 5.988 pounds