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 = - 0.09t^2 + 7.4t + 770.4 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)?
b. according to the formula, a workers median weekly earnings 3 months into 2020 was $861.15. this is the estimate found in part (a). (type an integer or a decimal )

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 (Median Weekly Earnings). By visual inspection of the line graph, when $t = 15$, the median weekly earnings seem to be around $\$860$.

Step2: Use the formula

The formula is $d=-0.09t^{2}+7.4t + 770.4$, and we substitute $t = 15$ into it.
\[

$$\begin{align*} d&=-0.09\times(15)^{2}+7.4\times15 + 770.4\\ &=-0.09\times225+111+770.4\\ &=-20.25+111 + 770.4\\ &=(-20.25+111)+770.4\\ &=90.75+770.4\\ &=861.15 \end{align*}$$

\]

Step3: Compare the results

The estimate from the graph is approximately $\$860$ and the value from the formula is $\$861.15$. The value from the formula is slightly higher than the estimate from the graph.

Answer:

a. Approximately $\$860$
b. $\$861.15$. The value from the formula is slightly higher than the estimate from the graph.