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

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    2021-09-12T06:25:10+00:00

    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;

    f(t)=5g

    but at a time t = 2

    f(2)=5g (t represents time)

    the expression for the rate of change (in grams/minute)

    f'(t)=-f(t)(1+f(t))

    subtituting the value of f(t) into the expression above

    =-4f(2)(1+f(2))

    we already showed that f (2) = 5, substituting this into the rate of change expression

    =-4(5)(1+5)\\=-20(1+5)\\=-20-100\\=-120grams/minute

    converting this into second, we will need to divide by 60 second

    \frac{-120}{60} \\=-2g/s

    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

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