Question

PLEASE HELP

Sarah gets a job paying $32,000 a year with the promise of a pay increase of 4% per year.

a. Write a recursive routine to help find Sarah's yearly pay each year.
Start with: 32000
Rule: Multiply by 1.04

b. To the nearest dollar, how much will Sarah make year 5?



c. During what year will Sarah first make more than $40,000 per year?

Answer 1

• a) P(x) = 32000*1.04^x
• b) $37435
• c) During year 7

Explanation:

Given

• Initial pay = $32000
• Increase rate = 4%

a. Formula

• P(x) = 32000*1.04^x

b. Year 5 is after 4 years, so we are looking for the value of P(4)

• P(4) = $32000*1.04^4 = $37435

c. P(x) = 40000, x = ?

• 40000 = 32000*1.04^x
• 1.04^x = 40000/32000
• 1.04^x = 1.25
• log 1.04^x = log 1.25
• x = log 1.25 / log 1.04
• x = 5.69, this is 6 years after

The required number of the years is 6 + 1 = 7