The chance that any given bulb is on is equal to 1/2. The chance that all twenty bulbs are on at the same time is
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](https://tex.z-dn.net/?f=n%20%3D%2026.8%280.85%29%5Et)
Solving (a): The decay factor
An exponential function has the form
![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
Where b is:
![b = decay\ factor\ or\ growth\ factor](https://tex.z-dn.net/?f=b%20%3D%20decay%5C%20factor%5C%20or%5C%20growth%5C%20factor)
By comparison:
![b = 0.85](https://tex.z-dn.net/?f=b%20%3D%200.85)
Solving (b): Percentage decrease:
Percentage decrease P is calculated as follows:
![P = 1 - b](https://tex.z-dn.net/?f=P%20%3D%201%20-%20b)
Substitute 0.85 for b
![P = 1 - 0.85](https://tex.z-dn.net/?f=P%20%3D%201%20-%200.85)
![P = 0.15](https://tex.z-dn.net/?f=P%20%3D%200.15)
Convert to percentage
![P = 0.15*100\%](https://tex.z-dn.net/?f=P%20%3D%200.15%2A100%5C%25)
![P = 15\%](https://tex.z-dn.net/?f=P%20%3D%2015%5C%25)
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](https://tex.z-dn.net/?f=n%20%3D%2026.8%280.85%29%5Et)
![n = 26.8(0.85)^2](https://tex.z-dn.net/?f=n%20%3D%2026.8%280.85%29%5E2)
![n = 26.8*0.7225](https://tex.z-dn.net/?f=n%20%3D%2026.8%2A0.7225)
![n = 19.363](https://tex.z-dn.net/?f=n%20%3D%2019.363)
Answer:
60%
Step-by-step explanation:
A 40% discount means that 40% will be off, meaning you won't have to pay 40% of the original price. Therefore, you only pay 60% of the original price (100% - 40% = 60%).