Let f (t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid dissolves in such a way that the ROC (in grams/min) of the weight of the solid at any time 't'

Question

Let f (t) be the weight (in grams) of a solid sitting in a beaker of water. 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 formula: f ' (t) = (-2)*(f(t))*(4 + f(t)).

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

I'm so confused. I just learned linear approximation and differentials and somehow that is supposed to relate to this question, which isn't making sense to me. Can somebody please help me understand how to solve this problem?

Answer 1

I assume that t = 2 is in minutes and 1 second is 1/60 minute. The formula is

f(2+1/60) = f(2) + delta f = f(2) + f'(2) delta t = 6 + f'(2)(1/60)

Just calculate f'(2) and find f(2 + 1/60).