Bluebook SAT Test Two-Variable Data: Models and Scatterplots 5

Question 1

The model y = 200(0.85)^x represents the number of bacteria (y) after x hours. What type of model is this and what is happening to the population?

Accepted Answer

Exponential decay; the population is decreasing

Answer

The base 0.85 is between 0 and 1, making this exponential decay — the population decreases by 15% each hour.

Question 2

A data point at (4, 30) lies above the line of best fit y = 5x + 6. What is the residual?

Accepted Answer

4

Answer

Predicted y = 5(4) + 6 = 26; residual = 30 − 26 = 4.

Question 3

A line of best fit for the data x: 1, 2, 3, 4, 5 and y: 7, 9, 11, 13, 15 is y = mx + b. What is m?

Accepted Answer

2

Answer

The y values increase by 2 for every unit increase in x, so the slope m = 2.

Question 4

Which correlation coefficient indicates the weakest linear relationship?

Accepted Answer

r = −0.02

Answer

The value closest to 0 (r = −0.02) indicates the weakest linear relationship.

Question 5

Using a line of best fit to predict y for an x value far outside the range of the data is called extrapolation. Why is this risky?

Accepted Answer

The model may not accurately represent the relationship outside the observed range

Answer

Extrapolation is unreliable because the pattern established in the data range may not continue outside it.

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