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Module Four Test Part 2

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Question 1 (10 points)

Part A: Use the properties of exponents to explain why is called the fourth root of 16. (5 points)
Part B: The length of a rectangle is 5 units and its width is unit. Is the area of the rectangle rational or irrational? Justify your answer. (5 points)
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Question 2 (10 points)

A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days: f(n) = 15(1.04)n
Part A: When the scientist concluded his study, the height of the plant was approximately 20.53 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points)
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Question 3 (10 points)

The price of products may increase due to inflation and decrease due to depreciation. Derek is studying the change in the price of two products, A and B, over time.
The price f(x), in dollars, of product A after x years is represented by the function below. f(x) = 12500(0.82)x
Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the price f(t), in dollars, of product B after t years: t (number of years) 1 2 3 4 f(t) (price in dollars) 5600 3136 1756.16 983.45
Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points) Question 3 options:

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Question 4 (10 points)

Fiber-optic cables are used widely by broadcast...

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