Which ordered pairs lie on the graph of the exponential function f(x)=−3^(x−1) +2 Select each correct answer.
1 answer:
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The scatter graph of the data is shown in the first picture below
The 'line of best fit' shows a negative gradient
Part A: The most likely coefficient is -0.98.
If the coefficient is -1, then each point would be exactly on the straight line (which they are not as shown on the graph). The graph however still shows a strong negative coefficient. It can be seen from the close distance of each point from the line of best fit. So -0.5 and -0.02 is unlikely as they show weak negative correlation
Part B: Refer to the second picture to see the horizontal and vertical distance between day 15 and day 20
The horizontal distance is 5 units
The vertical distance is read between 61 and 71.5, hence it's 10.5
The slope = Vertical distance ÷ Horizontal Distance = 10.5÷5 = 2.1
The 'downhill' slope shows a negative gradient, hence the value of the slope is -2.1
The value of the slope shows that the surface area of the lake shrinks by 2.1 for every one day
Part C: The data in the table represents the relation between two variables. Since one variable doesn't cause the change in the other variable, the data table represents correlation rather than a causation.
The 'line of best fit' shows a negative gradient
Part A: The most likely coefficient is -0.98.
If the coefficient is -1, then each point would be exactly on the straight line (which they are not as shown on the graph). The graph however still shows a strong negative coefficient. It can be seen from the close distance of each point from the line of best fit. So -0.5 and -0.02 is unlikely as they show weak negative correlation
Part B: Refer to the second picture to see the horizontal and vertical distance between day 15 and day 20
The horizontal distance is 5 units
The vertical distance is read between 61 and 71.5, hence it's 10.5
The slope = Vertical distance ÷ Horizontal Distance = 10.5÷5 = 2.1
The 'downhill' slope shows a negative gradient, hence the value of the slope is -2.1
The value of the slope shows that the surface area of the lake shrinks by 2.1 for every one day
Part C: The data in the table represents the relation between two variables. Since one variable doesn't cause the change in the other variable, the data table represents correlation rather than a causation.