https://file.aiquickdraw.com/mathbot/file/1726670227936cweik691.jpg

Let's break down and solve the problem based on the information provided in the image.

### Information:
- The mathematical model given is:
  \[
  d = -0.09t^2 + 7.5t + 770.8
  \]
  where $ d $ represents the worker's median weekly earnings in dollars, and $ t $ is the number of months after the beginning of 2019.

### Part (a):
- You are asked to **estimate** the worker's median weekly earnings **3 months into 2020**, which corresponds to **15 months** since the beginning of 2019 (because 12 months of 2019 + 3 months into 2020 = 15 months).
- According to the image, the line graph estimates that the median weekly earnings for this time is **\$863.05** (rounded to the nearest ten dollars).

### Part (b):
- Use the formula to find the worker's median weekly earnings **3 months into 2020**, i.e., when $ t = 15 $.

Substitute $ t = 15 $ into the equation:
\[
d = -0.09(15)^2 + 7.5(15) + 770.8
\]

Let's calculate this.

Use the line graph to estimate a worker's median weekly earnings 3 months into 2020 (i.e., 15 months since the beginning of 2019) and compare with the calculated result from the given quadratic formula.

Learn how to estimate a worker's median weekly earnings 15 months after the start of 2019 using a line graph and calculate it using the quadratic formula. The problem covers quadratic models and graph interpretation, suitable for students in Grades 9-12.

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