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)? b. according to the formula, a workers median weekly earnings 3 months into 2020 was $910. this is the estimate found in part (a) (type an integer or a decimal).

Explanation:

Step1: Estimate from the graph

By looking at the line - graph at \(t = 15\) months, we can estimate the median weekly earnings. Visually, it appears to be around \(925\) dollars.

Step2: Calculate using the formula

The formula is \(d=-0.09t^{2}+7.4t + 820.1\). Substitute \(t = 15\) into the formula.
\[

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

\]

Step3: Compare the results

The estimate from the graph is about \(925\) dollars and the value from the formula is \(910\) dollars. The value from the formula is less than the estimate from the graph.

Answer:

a. Approximately \(925\) dollars
b. \(910\) dollars; less than