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

Step-by-step 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: $n = 26.8(0.85)^t$

$n = 26.8(0.85)^2$

$n = 26.8*0.7225$

$n = 19.363$