Question

When Joseph first starts working at a grocery store, his hourly rate is \$10$10dollar sign, 10. For each year he works at the grocery store, his hourly rate increases by \$0.50$0.50dollar sign, 0, point, 50. Joseph's hourly rate RRR, in dollars, is a function of ttt, the number of years he works at the grocery store. Write the function's formula.

Answer 1

0.5t+10

Explanation:

The yearly increase to Joseph's hourly rate is constant, so we're dealing with a linear relationship.

We could write the desired formula in slope-intercept form: R=mt+b. in this form, m gives us the slope of the graph of the function and b gives us the values of m and b and substitute them into this formula.

We know that for each year Joseph works at the grocery store, his hourly rate increases by 0.50, so the slope m is 0.5 and our function looks like R= 0.5+b.

We also know that his starting hourly rate is $10 dollar sign, 10, so the y-intercept b is 10.

Answer 2

`R(t)=10+0.50t`

Explanation:

Let t represent the number of years.

We have been given that When Joseph first starts working at a grocery store, his hourly rate is $10.

For each year he works at the grocery store, his hourly rate increases by $0.50. Increase in hourly rates after t years would be
`0.50t`

The hourly rates after t years will be 10 plus
`0.50t`.

We can represent this information in an equation as:

`R(t)=10+0.50t`

Therefore, the function
`R(t)=10+0.50t` represents Joseph's hourly rates after t years.