Question

A construction worker's starting salary is $31,500. Each year she recieves a $850 raise. A) Let aₙ be the construction worker's salary in the nth year. Write an explicit formula of the form aₙ​=bn+c to model this situation. aₙ​=1 B) Find α10​=$ C) In what year will her salary be $42,550 ? Question Help: □ Message instructor

Answer 1

The explicit formula to model the construction worker's salary is a_n = 850n + 31,500. Her salary in the 10th year, α_10, is $40,000. Her salary will be $42,550 in the 13th year.

Step-by-step explanation:

The explicit formula to model the construction worker's salary is an = 850n + 31,500. To find α10, plug in n = 10 into the formula: a10 = 850(10) + 31,500 = $40,000. To find the year when her salary is $42,550, set an = 42,550 and solve for n: 42,550 = 850n + 31,500. Subtract 31,500 from both sides to get 11,050 = 850n. Divide both sides by 850 to get n = 13. Therefore, her salary will be $42,550 in the 13th year.