Properties of exponents | Algebra homework help

Question 1 


Part A: Use the properties of exponents to explain why 64 raised to the power of 1 over 2 is called the square root of 64. (5 points)

Part B: The length of a rectangle is 7 units and its width is square root of 7 unit. Is the area of the rectangle rational or irrational? Justify your answer. (5 points)




Question 2 


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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)




Question 3 


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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) = 0.69(1.03)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) 10,100 10,201 10,303.01 10,406.04

Which product recorded a greater percentage change in price over the previous year? Justify your answer. 





Question 4 


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Fiber-optic cables are used widely to increase the speed and accuracy of data transmission. When light passes through a fiber-optic cable, its intensity decreases with the increase in the length of the cable. If 1700 lumens of light enters the cable, the intensity of light decreases by 1.9% per meter of the cable.

Part A: Can this situation be represented by a linear function? Justify your answer. (2 points)

Part B: Write a function f(x) to represent the intensity of light, in lumens, when it has passed through x meters of the cable. (4 points)

Part C: Some scientists are trying to make a cable for which the intensity of light would decrease by 2 lumens per unit length of the cable. Can this situation be represented by a linear function? Justify your answer and write the appropriate function to represent this situation if 1700 lumens of light enter the cable. (4 points)




Question 5 


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Belinda wants to invest $1000. The table below shows the value of her investment under two different options for two different years:

Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331

Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)

Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda’s investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)


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