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60 POINTS, BOTH PARTS

Part A

BUSINESS: Ahmed's consulting firm began with 23 clients. The number of clients decrease at an annual rate of 0.5%.

Write a function that represents the number of clients at Ahmed's consulting firm y after x years.

A) y = 24(0.995)^x
B) y = 24(1.995)^x
C) y = 23(1.995)^x
D) y = 23(0.995)^x

Part B

After how many years will Ahmed's consulting firm have 15 clients? Round to the nearest year if necessary.

Respuesta :

mhanifa

Answer:

  • D) y = 23(0.995)^x
  • 85 years

Step-by-step explanation:

Part A

  • Initial number of clients = 23
  • Decrease rate = 0.5%
  • Time = x years

Required function:

  • y = 23(1 - 0.5/100)^x = 23(0.995)^x

Part B

y = 15, x = ?

  • 15 = 23(0.995)^x
  • (0.995)^x = 15/23
  • (0.995)^x = 0.65217391304
  • x log 0.995 = log 0.65217391304
  • x = log 0.65217391304 / log 0.995
  • x = 85 years

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