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Cynthia works at a factory where they make ties.At the beginning of the day as Cynthia greets other workers and gathers her materials, she gets little done. At the end of the day as she gets fatigued and as she cleans up her work station, her production drops off. The number of ties Cynthia makes each hour can be modeled by the equation b=5t−0.625t^2 where b is the number of ties and t is the number of hours since she begins her shift.

What is a reasonable domain and a reasonable range for this situation?

Respuesta :

MrRoyal

The reasonable domain is 0 <= t <= 8 and the reasonable range is 0 <= b <= 10

What is a reasonable domain and a reasonable range for this situation?

The domain

The equation of the function is:

b = 5t − 0.625t^2

Set the function to 0

5t − 0.625t^2 = 0

Divide through by 5t

1 − 0.125t = 0

This gives

0.125t = 1

Solve for t

t = 8

This means that the reasonable domain is 0 <= t <= 8

The range

The equation of the function is:

b = 5t − 0.625t^2

Differentiate the function and set to 0

5 − 1.25t = 0

Evaluate the like terms

1.25t = 5

Solve for t

t = 4

Substitute t = 4 in b = 5t − 0.625t^2

b = 5 * 4 − 0.625 * 4^2

Evaluate

b = 10

Hence, the reasonable range is 0 <= b <= 10

Read more about domain and range at:

https://brainly.com/question/28048756

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