Aquality assurance specialist makes $22 an hour for the first 40 hours she works during a week and $29 an hour for each hour worked over 40 hours. which piecewise equation models her total weekly pay y in dollars as it relates to the number of hours x that she has worked during the week?

We want to write a piecewise function that models how much the specialist wins per week. The piecewise function is:

f(x) = $22*x   →   if   x ≤ 40

f(x) = $29*(x - 40) + $880   →   if  x < 40

It is a function that behaves differently in different parts of the domain.

Here, we can define x as the number of hours, so for x smaller or equal than 40, the function is:

f(x) = $22*x

For x larger than 40, the function will be:

f(x) = $29*(x - 40) + $22*40

Because she gets paid extra for each hour after the 40th one.

The piecewise function is written as:

f(x) = $22*x   →   if   x ≤ 40

f(x) = $29*(x - 40) + $880   →   if  x < 40

This is the wanted piecewise function.

If you want to learn more about piecewise functions, you can read:

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let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt