Question

Jing just got a new job. She started at a pay rate of $12.50 per hour and will get a $0.50 raise each year. Max started a job where his salary is found by the equation: f(x) = x + 10 , where x is the number of years.

Interpret the rates of change and initial values of the linear functions in terms of the situations they model. Compare the results and what they mean. How many years must they both work for Max to earn more per hour than Jing?

Jing

Initial value:

Rate of change:

Max

Initial value:

Rate of change:

Answer 1

Jing's initial pay rate is $12.50 per hour. She will receive a pay raise of $0.50 per hour every year.

Max's initial pay rate is 10 dollars per hour. He will receive a pay raise of 1 dollar per hour every year.

To determine how many years it will take for Max to earn more per hour than Jing, we need to find the point at which the two linear equations intersect. This can be done by setting the two equations equal to each other and solving for x.

Jing's equation is: $12.50 + 0.50x

Max's equation is: x + 10

Setting the equations equal to each other and solving for x, we get:

$12.50 + 0.50x = x + 10

This simplifies to:

$0.50x = -2.50

Dividing both sides by 0.50, we get:

x = -5

Since the value of x cannot be negative, this means that Max will never earn more per hour than Jing.