Question: The MyTunes song app sells music downloads. Over the past few years, the service has lowered its prices. The table shows the price per song and the number of songs downloaded per day at the price.
Price per Song
Number of Downloads (in thousands)
$0.89
1,212
$0.79
1,704
$0.69
1,760
$0.59
1,877
$0.49
1,944
$0.39
2,011
a. Examine the data without drawing a scatter plot. Describe any trends you see.
b. Describe the correlation.
c. Approximate the number of downloads at a price of $0.54 per song. Explain your reasoning.
1. **State the problem:** We have a table showing prices per song and corresponding downloads (in thousands). We need to analyze trends, describe correlation, and estimate downloads at $0.54 per song.
2. **Examine the data for trends:**
- As the price decreases from $0.89 to $0.39, the number of downloads increases from 1,212 to 2,011.
- This suggests a negative relationship: lower price leads to more downloads.
3. **Describe the correlation:**
- The data shows a strong negative correlation between price and downloads.
- As price decreases, downloads increase consistently.
4. **Approximate downloads at $0.54:**
- The price $0.54 lies between $0.59 and $0.49.
- Downloads at $0.59 are 1,877 and at $0.49 are 1,944.
- Use linear interpolation:
$$\text{Downloads at } 0.54 = 1877 + \frac{0.59 - 0.54}{0.59 - 0.49} \times (1944 - 1877)$$
5. **Calculate interpolation:**
$$= 1877 + \frac{0.05}{0.10} \times 67 = 1877 + 0.5 \times 67 = 1877 + 33.5 = 1910.5$$
6. **Interpretation:**
- Approximately 1,911 thousand downloads occur at $0.54 per song.
**Final answer:**
- a. Downloads increase as price decreases.
- b. There is a strong negative correlation.
- c. Estimated downloads at $0.54 price is about 1,911 thousand.