Question

Question 1

Sione just landed a great job as an engineer where he will make $55,000 a year. The

company he will work for guarantees a 3% pay increase each year so it's employees

salaries keep up with inflation. At the end of the 1* year Slone will have made $55,000

dollars.

1. What is the recursive function that will represent this situation?

a. m(t) = m(t - 1) + 0.03, m(1) = 55000

b. m(t) = m(t-1). 0.03, m(1) - 55000

c. m(t) = m(t-1) + 1.03, m(1) - 55000

d. m(t) = m(t-1). 1.03, m(1) = 55000

Answer 1

Option (d)

Explanation:

If the current salary of Sione is represented by the function m(t - 1),

Next year his salary m(t) gets hike of 3%.

So, the next year salary of Sione will be represented by,

m(t) = m(t - 1) + 3% of m(t - 1)

= m(t - 1) + 0.03 × m(t - 1)

= m(t - 1)(1 + 0.03)

= 1.03m(t - 1)

Since, at the end of year 1 his salary was $55000,

Recursive function will be,

m(t) = 1.03m(t - 1) = 55000

Therefore, Option (d) will be the answer.