After 2 hours, there are 1,400 mL of fluids remaining in a patient’s IV. The fluids drip at a rate of 300 mL per hour. Let x be the time passed, in hours, and y be the amount of fluid left in the IV, in mL. Write a linear function that models this scenario.

For the linear function of patent's IV and volume of fluid the slope is -300 and y intercept is 2000. The linear function that models given scenario is,

[tex]f(s)=-300x+2000[/tex]

What is linear function?

Linear function is the function in which the highest power of the unknown variable is one. Linear functions are used to model the real life problem in the mathematical expressions.

The linear function with dependent variable y and independent variable x can be written as,

[tex]y=mx+c[/tex]

Here, [tex]m[/tex] is the slope of the function and [tex]c[/tex] is the y intercept.

Given information-

Total fluid remain in patient’s IV after 2 hours is 1400 ml.

The rate of fluids drip is 300 ml per hour.

Variable x be the time passed, in hours, and variable y be the amount of fluid left in the patient's IV.

As the rate of fluids drip is 300 ml. It means the value of variable y is changing with 300 times the value of x. Thus the slope of the line is -300.

Put in the above equation as,

[tex]y=-300x+c[/tex]

Negative sign indicates that the volume is decreasing.

As the rate of fluid drip is 300 ml per hour. The total amount of fluid drip in 2 hours is,

[tex]v=300\times2\\v=600[/tex]

Now the amount of fluid before 2 hours is,

[tex]V=1400+600\\V=2000[/tex]

Thus the y intercept of equation is 200. Put the value in the equation as,

[tex]y=-300x+2000[/tex]

Hence the linear function that models given scenario is,

[tex]f(s)=-300x+2000[/tex]

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