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Maths-

General

Easy

Question

After diluting salt water, the concentration of salt in the water is given by the function $f left parenthesis x right parenthesis equals fraction numerator 0.5 x over denominator x squared minus 1 end fraction$ , where x is the time in hours since the dilution.
b. After how many hours will the concentration of salt in the water be ?Round to the nearest hundredth.

The correct answer is: After 3 hours the concentration of salt in water will be 0.2.

We have given the value of f(x) = 0.2
0.2 = 0.5x/ x²- 1
0.2(x²- 1) = 0.5x
0.2x²- 0.2 – 0.5x = 0
2x² – 5x – 2 = 0
$straight x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$
$fraction numerator negative left parenthesis negative 5 right parenthesis plus-or-minus square root of left parenthesis negative 5 right parenthesis squared minus 4 left parenthesis 2 right parenthesis left parenthesis negative 2 right parenthesis end root over denominator 2 left parenthesis 2 right parenthesis end fraction$
$fraction numerator 5 plus-or-minus square root of 25 plus 16 end root over denominator 4 end fraction$
$fraction numerator 5 plus-or-minus square root of 41 over denominator 4 end fraction$
= 2.85
= 3
After 3 hours the concentration of salt in water will be 0.2.

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After diluting salt water, the concentration of salt in the water is given by the function $f left parenthesis x right parenthesis equals fraction numerator 0.5 x over denominator x squared minus 1 end fraction$ , where x is the time in hours since the dilution .
a. What is the concentration of salt in the water after 4 hours?

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