Question

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.

Answer 1

• D) y = 23(0.995)^x
• 85 years

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