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 + 920.6 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 graph

Locate $t = 15$ on the x - axis of the line - graph. Then, read the corresponding value on the y - axis. By observing the graph, when $t = 15$, the median weekly earnings $d$ is approximately $\$1000$.

Step2: Use the formula

The formula is $d=-0.09t^{2}+7.4t + 920.6$, and we substitute $t = 15$ into it.
\[

$$\begin{align*} d&=-0.09\times(15)^{2}+7.4\times15 + 920.6\\ &=-0.09\times225+111 + 920.6\\ &=-20.25+111+920.6\\ &=(-20.25)+(111 + 920.6)\\ &=-20.25 + 1031.6\\ &=1011.35\approx1010 \end{align*}$$

\]

Step3: Compare the results

The estimate from the graph is about $\$1000$, and the value from the formula is about $\$1010$. The value from the formula is $\$10$ more than the estimate from the graph.

Answer:

a. $1000$
b. The value from the formula is $1010$. The value from the formula is $10$ more than the estimate from the graph.