Question

49. When a store releases a new cell phone to customers, it expects its sales to decrease by 5% each month after the initial month. If the store sells 682 of a particular phone the first month, which exponential function models this situation x months after the initial month?

A f(x) = 682 • 1.05^x
B f(x) = 682 • 0.05^x
C f(x) = 682 • 0.95^x
D f(x) = 682 • 1.95^x​

Answer 1

C) f(x)= 682 • 0.95^x

Explanation:

The formula for Exponential Decrease is given as:

y = a(1 - r)^x

Where

y = f(x)

a = Initial size of the population = 682

r = Growth rate = 5% = 0.05

x = Time is years

Therefore, our equation can be written as:

f(x) = 682 × (1 - 0.05)^x

f(x) = 682 × (0.95)^x

Therefore, the exponential function that models this situation x months after the initial month is

option C)

f(x) = 682 • 0.95^x