Question

Which of the following functions best models the data represented by the scatterplot shown below?

A scatter plot shows x values from 0 to 18 and y values from 0 to 3000 with 10 data points showing a positive relationship. The points are at (7, 402), (13, 1362), and (11, 978).

A. y=25x + 20

B. y= 8x^2 + 10

C. y= 2^x + 12

D. y= 160x - 100

Answer 1

To determine which of the given functions best models the data represented by the scatterplot, we need to consider both the nature of the data (which shows a positive relationship) and the specific data points provided.

The data points mentioned are:
- (7, 402)
- (11, 978)
- (13, 1362)

We can evaluate each function by substituting the x-values from the data points into the equations and seeing which function produces y-values closest to those in the data points.

### Evaluating each option:

**A. y = 25x + 20**

- For x = 7: y = 25(7) + 20 = 175 + 20 = 195
- For x = 11: y = 25(11) + 20 = 275 + 20 = 295
- For x = 13: y = 25(13) + 20 = 325 + 20 = 345

**Results:** Not close to the y-values.

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**B. y = 8x^2 + 10**

- For x = 7: y = 8(7^2) + 10 = 8(49) + 10 = 392 + 10 = 402
- For x = 11: y = 8(11^2) + 10 = 8(121) + 10 = 968 + 10 = 978
- For x = 13: y = 8(13^2) + 10 = 8(169) + 10 = 1352 + 10 = 1362

**Results:** Matches all the given y-values (402, 978, 1362) exactly.

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**C. y = 2^x + 12**

- For x = 7: y = 2^7 + 12 = 128 + 12 = 140
- For x = 11: y = 2^11 + 12 = 2048 + 12 = 2060
- For x = 13: y = 2^13 + 12 = 8192 + 12 = 8204

**Results:** Not close to the y-values.

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**D. y = 160x - 100**

- For x = 7: y = 160(7) - 100 = 1120 - 100 = 1020
- For x = 11: y = 160(11) - 100 = 1760 - 100 = 1660
- For x = 13: y = 160(13) - 100 = 2080 - 100 = 1980

**Results:** Not close to the y-values.

### Conclusion:
The function that best models the data represented by the scatterplot is **B. y = 8x^2 + 10**. It matches the provided points exactly.