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 + 7.5t + 820.3 describes a worker’s median weekly earnings, d, in dollars, reported t months after the beginning of 2019.
a. use the line graph to estimate a worker’s median weekly earnings 3 months into 2020 (that is, 15 months since the beginning of 2019).
b. use the formula to find a worker’s median weekly earnings 3 months into 2020. how does this compare with the estimate in part (a)?
a. according to the line graph, a worker’s median weekly earnings 3 months into 2020 was about $ . (round to the nearest ten as needed )

Explanation:

Step1: Estimate from the graph

Locate the point at \(t = 15\) on the x - axis (months since beginning of 2019) on the line - graph. Then, read the corresponding value on the y - axis (median weekly earnings). By visual inspection of the line - graph, when \(t=15\), the median weekly earnings is about \(\$950\).

Step2: Use the formula

The formula is \(d=-0.09t^{2}+7.5t + 820.3\), and we substitute \(t = 15\) into it.
\[

$$\begin{align*} d&=-0.09\times(15)^{2}+7.5\times15 + 820.3\\ &=-0.09\times225+112.5 + 820.3\\ &=-20.25+112.5+820.3\\ &=(-20.25 + 112.5)+820.3\\ &=92.25+820.3\\ &=912.55\approx910 \end{align*}$$

\]
The estimate from the graph (\(\$950\)) is higher than the value from the formula (\(\$910\)).

Answer:

a. \(950\)
b. The value from the formula is about \(\$910\). The estimate from the graph (\(\$950\)) is higher than the value from the formula.