Math Problem Statement

Complete the table with the functions y = 2x^2 and y = 2^x for values of x = 0, 1, and 2.

Solution

To complete the table in the image, we need to evaluate the given functions y=2x2y = 2x^2 and y=2xy = 2^x for the values of xx.

Function 1: y=2x2y = 2x^2

  • When x=1x = 1: y=2(1)2=2(1)=2y = 2(1)^2 = 2(1) = 2
  • When x=2x = 2: y=2(2)2=2(4)=8y = 2(2)^2 = 2(4) = 8

Function 2: y=2xy = 2^x

  • When x=1x = 1: y=21=2y = 2^1 = 2
  • When x=2x = 2: y=22=4y = 2^2 = 4

Now, let's update the table:

\hline x & y = 2x^2 & y = 2^x \\ \hline 0 & 0 & 1 \\ \hline 1 & 2 & 2 \\ \hline 2 & 8 & 4 \\ \hline \end{array}$$ Let me know if you'd like more details or explanations on these calculations! ### Related questions: 1. How do you derive the formula $$y = 2x^2$$? 2. Can you graph the function $$y = 2x^2$$ for better understanding? 3. What is the general form of exponential functions like $$y = 2^x$$? 4. What happens to $$y = 2x^2$$ as $$x$$ increases or decreases? 5. How does $$y = 2^x$$ differ from $$y = 2x^2$$ in growth rate? **Tip:** When working with functions, identifying patterns in the numbers (like quadratic vs. exponential growth) can help with predicting future values easily.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponential Growth
Quadratic Functions

Formulas

y = 2x^2
y = 2^x

Theorems

Laws of Exponents
Quadratic Function Behavior

Suitable Grade Level

Grades 6-8

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