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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?

Sagot :

Mhanifaidn

Answer:

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

Step-by-step 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

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