Question

In 2016, 50 million CDs were sold, representing a decline of 11.6% over the same period in the previous year. Assume that this trend continues. Enter an equation that represents the estimated sales in millions of units y after t years.

Answer 1

To estimate future CD sales based on a trend of an 11.6% annual decline, the exponential decay equation y = 50(1 - 0.116)^t could be used, where y represents the sales in millions and t is the number of years after 2016.

Step-by-step explanation:

The student is asking for an equation to estimate future CD sales in millions (y) after a certain number of years (t), based on a given annual decline rate.

Given that in 2016, there were 50 million CD sales and that this amount represents an 11.6% decline from the previous year, the decline rate is -11.6% per year.

To find an equation that represents this scenario, we use exponential decay, which can be expressed as:

y = a(1 - r)^t

Where:

• y is the estimated sales in millions of units
• a is the initial amount of CD sales at the starting point (50 million)
• r is the annual decline rate (11.6% or 0.116 as a decimal)
• t is the number of years after 2016

Substituting the given values, the equation becomes:

y = 50(1 - 0.116)^t

This equation can be used to predict the number of CDs sold in a given year after 2016, assuming the decline trend continues.