Algebra 2 Problems of the Day

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January 2019, Part II

All Questions in Part I are worth 2 credits. Partial credit can be earned.


29. Rowan is training to run in a race. He runs 15 miles in the first week, and each week following, he runs 3% more than the week before. Using a geometric series formula, find the total number of miles Rowan runs over the first ten weeks of training, rounded to the nearest thousandth.

Answer:
In the back of the booklet, you are given the formula for Geometric Series:

S_n = (a₁ - a₁rⁿ) / (1 - r)
Substitute n = 10 and r = 1.03 (103%)
S_n = (15 - 15(1.03)¹⁰) / (1 - 1.03)
= 171.958

30. The average monthly high temperature in Buffalo, in degrees Fahrenheit, can be modeled by the function

B(t) = 25.29 sin(0.4895t - 1.9752) + 55.2877,
where t is the month number (January = 1). State, to the nearest tenth, the average monthly rate of temperature change between August and November.

Explain its meaning in the given context.

Answer:
If January = 1, then August = 8 and November = 11.
To find the average rate of change, find B(11) - B(8) and divide it by (11 - 8).

B(11) = 25.29*sin(0.4895(11) - 1.9752) + 55.2877 = 48.59796...
B(8) = 25.29*sin(0.4895(8) - 1.9752) + 55.2877 = 78.86622...
B(11) - B(8) = -30.268...
-30.268 / 3 = -10.089 = -10.1

This means that from August to November that the temperature in Buffalo drops an average of 10.1 degrees Fahrenheit per month.



Comments and questions welcome.

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