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 + 820.1 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.)
b. according to the formula, a workers median weekly earnings 3 months into 2020 was $. this is the estimate found in part (a). (type an integer or a decimal.)

Explanation:

Step1: Estimate from graph

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

Step2: Use the formula

The formula for median weekly earnings is $d=-0.09t^{2}+7.4t + 820.1$, where $t = 15$.
Substitute $t = 15$ into the formula:
\[

$$\begin{align*} d&=-0.09\times(15)^{2}+7.4\times15 + 820.1\\ &=-0.09\times225+111 + 820.1\\ &=-20.25+111+820.1\\ &=(-20.25 + 111)+820.1\\ &=90.75+820.1\\ &=910.85\approx910 \end{align*}$$

\]

Step3: Compare the results

The estimate from the graph is $\$950$ and the value from the formula is $\$910$. So the value from the formula is less than the estimate from the graph.

Answer:

a. $950$
b. $910$; less than