Problem 24 - Basic College Mathematics

Question

Digital Downloads. There were 964.3 million songs downloaded in \(2015,\) and 723.7 million songs downloaded in 2016 . What was the percent decrease from 2015 to \(2016 ?\) Round to the nearest tenth of a percent. \([6.5 \mathrm{~b}]\)

Step-by-Step Solution

Answer

The percent decrease from 2015 to 2016 was 24.9%.

Step 1 - Identify the Initial and Final Values

Identify the number of songs downloaded in 2015 and 2016. For 2015, the number is 964.3 million and for 2016, the number is 723.7 million.

Step 2 - Calculate the Decrease in Downloads

Calculate the difference between the initial and final values: \[964.3 \text{ million} - 723.7 \text{ million} = 240.6 \text{ million}\]

Step 3 - Calculate the Percent Decrease

Use the percent decrease formula: \[\text{Percent Decrease} = \frac{{\text{Decrease in Value}}}{{\text{Initial Value}}} \times 100g:\frac{{240.6 \text{ million}}}{{964.3 \text{ million}}} \times 100= 24.95\text{\text{ million}}\]

Step 4 - Round to the Nearest Tenth

Round the result from Step 3 to the nearest tenth of a percent. \[24.9%\]

Key Concepts

percent change

Understanding how to calculate the percent change is a fundamental part of solving problems related to growth or decline. In this context, the percent decrease helps us understand how significantly the number of digital downloads has dropped from one year to the next. The formula for percent change is straightforward:
\(\text{Percent Change} = \frac{{\text{Change in Value}}}{{\text{Original Value}}} \times 100\).
In our exercise, the original value is the number of songs downloaded in 2015, and the new value is the number of songs downloaded in 2016.
By following through with the calculation, you'll determine how much the downloads have decreased on a percentage basis.
This gives a clearer understanding of the extent of change over time.

mathematical problem-solving

Mathematical problem-solving skills are essential for tackling exercises like these. Let's walk through the steps in the process to see how these skills come into play:

• First, identify the key values. In our problem, these are the downloads for 2015 and 2016.
• Next, compute the change by subtracting the final value (downloads in 2016) from the initial value (downloads in 2015).
• The formula for finding percent decrease is then applied using the difference found in the previous step divided by the initial value.
• Finally, convert this fraction to a percentage by multiplying by 100 and rounding as necessary.

Building proficiency in identifying the steps needed, performing calculations accurately, and rounding results properly can greatly improve one’s problem-solving capabilities.
Practice with these steps can help make math problems less intimidating and more approachable.

digital downloads statistics

Digital download statistics give us valuable insights into consumer behavior and trends over time. For instance, in this exercise, we see a decrease in song downloads from 2015 to 2016. This data can indicate various underlying factors, such as changes in consumer preferences, technological advancements, or the rise of alternative music consumption methods like streaming.
To better analyze digital download statistics, consider the following:

• Identify trends by looking at data over multiple years.
• Compare the changes year over year to understand the growth or decline.
• Consider external factors that might influence the statistics, such as new market entrants, changes in technology, or economic conditions.

By looking at these statistics holistically, we can derive meaningful interpretations that highlight not just the raw numbers but the stories they tell about the market and consumer behavior.
This broader understanding aids in making informed decisions, be it in business, marketing, or academic inquiries.