Scatter Plots and Exponential Curves

1. Given a set of data points, how would you create a scatter plot to represent the relationship between two variables?

• Plot the data points on a pie chart

• Plot the data points on a graph with the x-value on the horizontal axis and the y-value on the vertical axis.

• Use a bar graph instead of a scatter plot

• Connect the data points with straight lines

Tags

CCSS.8.SP.A.1

2. What does it mean if the points on a scatter plot form a clear pattern or trend?

• There is a relationship between the two variables being plotted.

• It means there is no relationship between the two variables

• It means the data is inaccurate

• It means the scatter plot is not a reliable graph

Tags

CCSS.HSS.ID.B.5

3. How can you use a line of best fit on a scatter plot to make predictions about the relationship between the variables?

• By extending the line to estimate the value of one variable based on the value of the other variable.

• By drawing a straight line through the center of the scatter plot

• By ignoring the line and focusing only on the individual data points

• By using the line to determine the maximum value of one variable

Tags

CCSS.8.EE.B.5

4. Explain the meaning of the slope and y-intercept of a line of best fit on a scatter plot.

• The slope represents the temperature and the y-intercept represents the time.

• The slope represents the rate of change and the y-intercept represents the value of y when x is 0.

• The slope represents the weight and the y-intercept represents the height.

• The slope represents the color of the line and the y-intercept represents the shape of the line.

Tags

CCSS.8.EE.B.5

5. Provide an example of a real-world scenario where an exponential function could be applied to represent the relationship between two variables.

• Temperature and distance

• Population growth and time

• Height and weight

• Speed and time

Tags

CCSS.HSF-LE.A.1A

6. How would you evaluate the goodness of fit for an exponential curve on a scatter plot?

• Calculate the coefficient of determination (R-squared) and examine the residual plot.

• Draw a line of best fit through the data points

• Find the average of the x and y values

• Count the number of data points

7. If an exponential curve has a high goodness of fit, what does that indicate about the relationship between the variables?

• The relationship between the variables is negative.

• The relationship between the variables is weak.

• There is no relationship between the variables.

• There is a strong relationship between the variables.

8. Describe a situation where the slope of an exponential curve would have a specific real-world meaning.

• Distance traveled by a car

• Population growth, radioactive decay, compound interest

• Temperature change over time

• Height of a building over time

9. What is the process for using an exponential curve to make predictions about future data points?

• Ignore the existing data and make random predictions

• Fit an exponential curve to the existing data and use the equation to predict future data points

• Fit a quadratic curve to the existing data and use the equation to predict future data points

• Use a linear curve to predict future data points

Tags

CCSS.HSF-LE.A.1A

10. Explain how the y-intercept of an exponential curve can be interpreted in the context of a real-world scenario.

• The y-intercept represents the rate of change in the real-world scenario.

• The y-intercept represents the initial value or starting point of the real-world scenario.

• The y-intercept represents the maximum value of the real-world scenario.

• The y-intercept has no real-world interpretation.

Tags

CCSS.HSF.LE.B.5