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Melissa's garden is growing! She notices her tomato plants were 2 inches the first week, 4 inches the second week, 8 inches the third week, and 16 inches the fourth week! Her tomato plant is doubling in size each week. She wants to be able to predict how tall it might be each week so she tries to write an equation to show the growth. She comes up with y=2x, where x is the number of weeks, and y is the height of the plant. 1. Does her equation work? Why or Why not? Show your calculations to prove if it works or not. 2. Sam comes over and tells Melissa her tomato plant is actually growing according to the equation y=x^2. Is Sam correct? Why or why not? Show your calculations to prove if it works or not.

Melissa's garden is growing! She notices her tomato plants were 2 inches the first week, 4 inches the second week, 8 inches the third week, and 16 inches the fourth week! Her tomato plant is doubling in size each week. She wants to be able to predict how tall it might be each week so she tries to write an equation to show the growth. She comes up with y=2x, where x is the number of weeks, and y is the height of the plant. 1. Does her equation work? Why or Why not? Show your calculations to prove if it works or not. 2. Sam comes over and tells Melissa her tomato plant is actually growing according to the equation y=x^2. Is Sam correct? Why or why not? Show your calculations to prove if it works or not.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Melissa's garden is growing! She notices her tomato plants were 2 inches the first week, 4 inches the second week, 8 inches the third week, and 16 inches the fourth week! Her tomato plant is doubling in size each week. She wants to be able to predict how tall it might be each week so she tries to write an equation to show the growth. She comes up with y=2x, where x is the number of weeks, and y is the height of the plant. 1. Does her equation work? Why or Why not? Show your calculations to prove if it works or not. 2. Sam comes over and tells Melissa her tomato plant is actually growing according to the equation y=x^2. Is Sam correct? Why or why not? Show your calculations to prove if it works or not.
Transcribed Image Text:Melissa's garden is growing! She notices her tomato plants were 2 inches the first week, 4 inches the second week, 8 inches the third week, and 16 inches the fourth week! Her tomato plant is doubling in size each week. She wants to be able to predict how tall it might be each week so she tries to write an equation to show the growth. She comes up with y=2x, where x is the number of weeks, and y is the height of the plant. 1. Does her equation work? Why or Why not? Show your calculations to prove if it works or not. 2. Sam comes over and tells Melissa her tomato plant is actually growing according to the equation y=x^2. Is Sam correct? Why or why not? Show your calculations to prove if it works or not.
3. Lance visits and tell Melissa that she and Sam are both wrong and she should come up with an exponential equation instead. What exponential equation could show the growth of Melissa's tomato plants? Prove that your equation works or does not work by showing your calculations. For example, y=5^x will not work because if x=1, y=5, and at week 1 the tomato plants were not 5 inches, they were 2 inches. 4. What if Melissa's bell peppers grew from 3 inches in week 1 to 9 inches in week 2 and 27 inches in week 3? Come up with an equation to show the growth of the bell peppers. Prove that it works by showing your calculations. 5. What pattern do you see in exponential equations? How can you tell if you should use the equation for a line (y=2x) versus the equation for a parabola (y=x^2) versus an exponential equation (y=2^x) from the values you are working with? Write a general rule for writing exponential equations.
Transcribed Image Text:3. Lance visits and tell Melissa that she and Sam are both wrong and she should come up with an exponential equation instead. What exponential equation could show the growth of Melissa's tomato plants? Prove that your equation works or does not work by showing your calculations. For example, y=5^x will not work because if x=1, y=5, and at week 1 the tomato plants were not 5 inches, they were 2 inches. 4. What if Melissa's bell peppers grew from 3 inches in week 1 to 9 inches in week 2 and 27 inches in week 3? Come up with an equation to show the growth of the bell peppers. Prove that it works by showing your calculations. 5. What pattern do you see in exponential equations? How can you tell if you should use the equation for a line (y=2x) versus the equation for a parabola (y=x^2) versus an exponential equation (y=2^x) from the values you are working with? Write a general rule for writing exponential equations.
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