## 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 o

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 forumula f'(t)=-4f(t)(1+f(t))
If there is 5 grams of solid at time t=2 estimate the amount of solid 1 second later.

in progress 0
2 weeks 2021-09-12T06:23:47+00:00 1 Answer 0

3 grams

Step-by-step explanation:

first of all

the weight in grams has been given to be f (t)

since there are 5 grams of solid in the beaker

then; but at a time t = 2 (t represents time)

the expression for the rate of change (in grams/minute) subtituting the value of f(t) into the expression above we already showed that f (2) = 5, substituting this into the rate of change expression converting this into second, we will need to divide by 60 second the weight is decreasing 2 g/s at a time 2 ( the minus sign shows decrease)

the amount of solid 1 second later will be

the amount of solid in the beaker subtract the amount of solid that dissolved

5 – 2 = 3 grams