the figure illustrates the growth in the net sales of an e - service company from 2018 through 2022. use the…
the figure illustrates the growth in the net sales of an e - service company from 2018 through 2022. use the midpoint formula to estimate the net sales of the e - service company in 2020. how does your result compare to the reported value of $358.44 billion? select the correct choice and fill in the answer box within your choice. (simplify your answer. type an integer or a decimal rounded to two decimal places as needed.) a. the midpoint estimate is $ billion. this underestimates the reported value. b. the midpoint estimate is $ billion. this overestimates the reported value.
Answer
- First, identify the points on the graph:
- The year 2018 corresponds to a net - sales value of (y_1 = 216.00) billion, and the year 2022 corresponds to a net - sales value of (y_2 = 516.07) billion.
- The mid - point formula for a linear interpolation between two points ((x_1,y_1)) and ((x_2,y_2)) to find the value at (x=\frac{x_1 + x_2}{2}) is (y=\frac{y_1 + y_2}{2}). Here, (x_1 = 2018), (x_2 = 2022), and we want to find the value at (x = 2020) (the mid - point between 2018 and 2022).
- Calculate the mid - point estimate:
- Using the mid - point formula (y=\frac{y_1 + y_2}{2}), substitute (y_1 = 216.00) and (y_2 = 516.07).
- (y=\frac{216.00+516.07}{2}=\frac{732.07}{2}=366.035\approx366.04) billion.
- Compare with the reported value:
- The reported value is (358.44) billion. Since (366.04>358.44), the mid - point estimate overestimates the reported value.