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## 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.

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Math
2 weeks
2021-09-12T06:23:47+00:00
2021-09-12T06:23:47+00:00 1 Answer
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## Answers ( )

Answer: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 secondthe weight is decreasing 2 g/s at a time 2 ( the minus sign shows decrease)

the amount of solid 1 second later will bethe amount of solid in the beaker subtract the amount of solid that dissolved

5 – 2 = 3 grams