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 + 770.2 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 the graph

By observing the line - graph at \(t = 15\) months, we visually estimate the median weekly earnings. Looking at the graph, when \(t=15\), the value of \(d\) (median weekly earnings) is approximately \(d\approx900\) dollars.

Step2: Use the formula

The formula is \(d=-0.09t^{2}+7.4t + 770.2\), and we substitute \(t = 15\) into it.

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Step3: Compare the results

The estimate from the graph is about \(900\) dollars and the value from the formula is about \(860\) dollars. The estimate from the graph is higher than the value calculated from the formula.

Answer:

a. \(900\)
b. The value from the formula is about \(860\) dollars. The estimate from the graph (\(900\) dollars) is higher than the value calculated from the formula.