Algebra 2 Problems of the Day (open-ended)

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January 2018, Part II

Questions in Part II are worth 2 credits. All work must be shown or explained for full credit. A correct numerical answer without work is only worth 1 credit.
Elizabeth tried to find the product of (2 + 4i) and (3 - i), and her work is shown below.

(2 + 4i)(3 - i)
= 6 - 2i + 12i - 4i²
= 6 + 10i - 4i²
= 6 + 10i - 4(1)
= 6 + 10i - 4
= 2 + 10i
Identify the error in the process shown and determine the correct product of (2 + 4i) and (3 - i).

Answer:
Elizabeth replaced i² with 1 instead of -1.
The correct answer is:

= 6 + 10i - 4(-1)
= 6 + 10i + 4
= 10 + 10i



26.A runner is using a nine-week training app to prepare for a “fun run.” The table below represents the amount of the program completed, A, and the distance covered in a session, D, in miles.

Based on these data, write an exponential regression equation, rounded to the nearest thousandth, to model the distance the runner is able to complete in a session as she continues through the nine-week program.

Answer:

Enter the data into two lists (L₁ and L₂, most likely). Check for errors.
Go to STAT, CALC and select ExpReg.
You should get the following output:
y = a*b^x
a = 1.223034549
b = 2.652024589
Round these numbers to the nearest thousandth. (You will lose a point if you do not round correctly.)
y = 1.223(2.652)^x.
You could have used A for x and D for y in your answer.



Comments and questions welcome.

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