Lloyd makes an hourly wage of $9.50 per hour. Every 6 months he receives a $0.50 per hour raise. Write a rule that describes his raise and determine how much he will be paid after 4 years.
Let n be the number of 6-month periods he is employed
wage = 9.5 + 0.5n
after 4 years (8 periods) he will make
9.5 + .5(8) = 9.5 + 4 = 13.50
To write a rule that describes Lloyd's raise, we need to understand the pattern.
Lloyd's hourly wage starts at $9.50 per hour. Every 6 months, he receives a $0.50 per hour raise. This means that after each 6-month period, his wage increases by $0.50.
We can determine Lloyd's wage after each 6-month period using the following formula:
Wage after Nth 6-month period = Initial wage + (Raise per 6-month period * N)
Where:
Initial wage = $9.50 per hour
Raise per 6-month period = $0.50 per hour
N = number of 6-month periods
Now, let's calculate Lloyd's wage after 4 years, which is equivalent to 8 six-month periods:
Wage after 8 six-month periods = $9.50 + ($0.50 * 8)
Wage after 8 six-month periods = $9.50 + $4.00
Therefore, Lloyd will be paid $13.50 per hour after 4 years.