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
[tex]n = 26.8(0.85)^t[/tex]
Solving (a): The decay factor
An exponential function has the form
[tex]y = ab^x[/tex]
Where b is:
[tex]b = decay\ factor\ or\ growth\ factor[/tex]
By comparison:
[tex]b = 0.85[/tex]
Solving (b): Percentage decrease:
Percentage decrease P is calculated as follows:
[tex]P = 1 - b[/tex]
Substitute 0.85 for b
[tex]P = 1 - 0.85[/tex]
[tex]P = 0.15[/tex]
Convert to percentage
[tex]P = 0.15*100\%[/tex]
[tex]P = 15\%[/tex]
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: [tex]n = 26.8(0.85)^t[/tex]
[tex]n = 26.8(0.85)^2[/tex]
[tex]n = 26.8*0.7225[/tex]
[tex]n = 19.363[/tex]
