Question

From 1997 - 2001 the number n (in millions) of black-and-white TV S sold in the U.S. Can be modeled by n = 26.8 * (0.85) ^ t where t is the number of years since 1997.

Answer 1

Question

a) What is the decay factor?

b) What is the percent decrease?

c) Estimate the number of black and white TV's sold in 1999.

Answer:

a. Decay factor = 0.85

b. Percent decrease = 15%

c. 19.363 million TVs were sold

Explanation:

Given

`n = 26.8(0.85)^t`

Solving (a): The decay factor

An exponential function has the form

`y = ab^x`

Where b is:

`b = decay\ factor\ or\ growth\ factor`

By comparison:

`b = 0.85`

Solving (b): Percentage decrease:

Percentage decrease P is calculated as follows:

`P = 1 - b`

Substitute 0.85 for b

`P = 1 - 0.85`

`P = 0.15`

Convert to percentage

`P = 0.15*100\%`

`P = 15\%`

Solving (c): TVs sold in 1999

First, we need to determine the value of t for 1999

In 1997, t= 0

In 1998, t= 1

In 1999, t= 2

So, we substitute 2 for t in:
`n = 26.8(0.85)^t`

`n = 26.8(0.85)^2`

`n = 26.8*0.7225`

`n = 19.363`