Algebra 2 Problems of the Day (Jan 2020)

Daily Algebra 2 questions and answers.

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January 2020, Part II

All Questions in Part II are worth 2 credits. Work must be shown. Partial credit is given.


31. Biologists are studying a new bacterium. They create a culture with 100 of the bacteria and anticipate that the number of bacteria will double every 30 hours. Write an equation for the number of bacteria, B, in terms of the number of hours, t, since the experiment began

Answer:
B(t) = 100(2)^t/30

Start with 100 bacteria. It's doubling, so the base is 2. The time is measured in hours, but it doubles every 30 hours, so the exponent is t/30.

32. Graph y = x³ - 4x² + 2x + 7 on the set of axes below.

Answer:
Put the equation in the calculator and check the table of values.
You'll see (-1, 0), (0, 7), (1, 6), (2, 3), (3, 4), (4, 15)
Also, you'll see (-2, 21), way below the screen, and (5, 42), which is way above.
Use this data to make the graph.
Also note that (2, 3) is not a minimum point, so when you sketch the curve, don't make it a turning point. Go through the point and curve after it.

Given the values, I used a scale of 1 on the x-axis and a scale of 2 on the y-axis. Label your scales.

Comments and questions welcome.

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