Analyzing Graphs

ID: rofuj-rupuk
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2
Grade: 8-9
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13 questions

Analyzing Graphs

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Problem 1

The two graphs show models characterized by exponential decay representing the area covered by two different algae blooms, in square yards, ww weeks after different chemicals were applied.

A template for answering this question. Ask your instructor for an alternative.

1) Which algae bloom covered a larger area when the chemicals were applied?

2) Explain how you know.

3) Which algae population is decreasing more rapidly?

4) Explain how you know.

Problem 2

A medicine is applied to a burn on a patient's arm. The area of the burn in square centimeters decreases exponentially and is shown in the graph.

A template for answering this question. Ask your instructor for an alternative.

5) What fraction of the burn area remains each week?

Show Work

6) Write an equation representing the area of the burn, aa, after tt weeks.

7) What is the area of the burn after 7 weeks? Round to three decimal places.

Show Work
Problem 3

8) The area of a sheet of paper is 100 square inches. Write an equation that gives the area, AA, of the sheet of paper, in square inches, after being folded in half nn times.

9) The area of another sheet of paper is 200 square inches. Write an equation that gives the area, BB, of this sheet of paper, in square inches, after being folded into thirds nn times.

10) Are the areas of the two sheets of paper ever the same after each being folded nn times?

True or false? Write below.

11) Explain how you know.

Problem 4

12) The graphs show the amounts of medicine in two patients after receiving injections. The circles show the medicine in patient A and the triangles show that in patient B.

One equation that gives the amount of medicine in milligrams, mm, in patient A, hh hours after an injection, is m=300(12)hm = 300 \left(\frac{1}{2}\right)^h.

What could be an equation for the amount of medicine in patient B?

A template for answering this question. Ask your instructor for an alternative.
a)

mm=500(310)h\left(\frac{3}{10}\right)^{h}

b)

mm=500(710)h\left(\frac{7}{10}\right)^{h}

c)

mm=200(310)h\left(\frac{3}{10}\right)^{h}

d)

mm=200(710)h\left(\frac{7}{10}\right)^{h}

Problem 5

13) Select all\textbf{all} expressions that are equivalent to 383^8. Write each corresponding letter in the answer box and separate letters with commas.

a) 32343^2 \cdot 3^4 \quad \quad b) 32363^2 \cdot 3^6 \quad \quad c) 31632\frac{3^{16}}{3^2} \quad \quad d) 31234\frac{3^{12}}{3^4} \quad \quad e) (34)2\left(3^4\right)^2 \quad \quad f) (31)7\left(3^1\right)^7 \quad \quad