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 + 921.3 describes a worker’s median weekly earnings, d, in dollars, reported t months after the beginning of 2019.
a. use the line graph to estimate a worker’s median weekly earnings 3 months into 2020 (that is, 15 months since the beginning of 2019).
b. use the formula to find a worker’s median weekly earnings 3 months into 2020. how does this compare with the estimate in part (a)?
a. according to the line graph, a worker’s median weekly earnings 3 months into 2020 was about $ 1000 (round to the nearest ten as needed.)
b. according to the formula, a worker’s median weekly earnings 3 months into 2020 was $ . this is the estimate found in part (a). (type an integer or a decimal.)

Explanation:

Step1: Identify the value of t

Since it's 15 months since the beginning of 2019, $t = 15$.

Step2: Substitute t into the formula

We have the formula $d=-0.09t^{2}+7.4t + 921.3$. Substitute $t = 15$ into it:
\[

$$\begin{align*} d&=-0.09\times(15)^{2}+7.4\times15 + 921.3\\ &=-0.09\times225+111+921.3\\ &=-20.25+111 + 921.3\\ &=90.75+921.3\\ &=1012.05 \end{align*}$$

\]

Step3: Compare with part (a)

The estimate in part (a) is $1000$, and the value from the formula is $1012.05$. So the value from the formula is greater than the estimate in part (a).

Answer:

$1012.05$; greater than