Which of the following equations best models the data shown in the scatterplot above?

Options

A. `y=(1)/(2)x`
B. `y=((1)/(2))^(x)`
C. `y=(1)/(2)(2^(x))`
D. `y=(3)/(2)x-1`

Answer

C

Explanation

Difficult: Medium
Category: Problem Solving and Data Analysis/ Scatterplots
Strategic Advice: Whenever you need to match data to a model, use the trend (shape) of the data to determine the type of model (linear, exponential, quadratic, or polynomial), and then use specific data points (if needed) to identify the best choice.
Getting to the Answer: The trend of the data shown in the scatterplot is increasing, slowly at first and then much more quickly, which indicates an exponential model. This means you can eliminate A and D (both are linear). To choose between B and (C), choose a data point (preferably one that lies on a grib-line and represents whole number values) and test it in each answer choice. Avoid x=0 and x=1 because those numbers habe special properties when exponential are involved. Using the point (3, 4), the result are:
`y=((1)/(2))^(x) to ((1)/(2))^(3)=(1)/(2)times(1)/(2)times(1)/(2)=(1)/(4)ne4`
Eliminate B, making (C) the correct choices. If you're still unsure, you can check (C):
`y=(1)/(2)*2^(x) to (1)/(2)*2^(3)=(1)/(2)*8=4`