Question

every 3 months, the government releases median weekly earnings of full - time wage and salary workers. the line graph shows the median weekly earnings of workers in the years 2019 and 2020. the mathematical model d = - 0.09t²+7.4t + 871.2 describes a workers median weekly earnings, d, in dollars, reported t months after the beginning of 2019.
a. use the line graph to estimate a workers median weekly earnings 3 months into 2020 (that is, 15 months since the beginning of 2019).
b. use the formula to find a workers median weekly earnings 3 months into 2020. how does this compare with the estimate in part (a)?
a. according to the line graph, a workers median weekly earnings 3 months into 2020 was about $ (round to the nearest ten as needed.)

Explanation:

Step1: Estimate from the graph

Locate the 15 - month mark on the x - axis of the line graph. Then, read the corresponding value on the y - axis. By visual inspection of the line graph, when \(t = 15\) (3 months into 2020), the median weekly earnings \(d\) is approximately \(\$1000\).

Step2: Use the formula

The formula for the median weekly earnings is \(d=-0.09t^{2}+7.4t + 871.2\), where \(t = 15\). Substitute \(t = 15\) into the formula:
\[

$$\begin{align*} d&=-0.09\times(15)^{2}+7.4\times15 + 871.2\\ &=-0.09\times225+111+871.2\\ &=-20.25+111 + 871.2\\ &=(-20.25+111)+871.2\\ &=90.75+871.2\\ &=961.95\approx960 \end{align*}$$

\]
The estimate from the graph (\(\$1000\)) is higher than the value calculated from the formula (\(\$960\)).

Answer:

a. \(1000\)
b. The value from the formula is about \(\$960\). The estimate from the graph (\(\$1000\)) is higher than the value calculated from the formula.