Math Problem Statement

Complete the missing parts of the table for the following function y = 5^x.

Solution

The given function is y=5xy = 5^x, and you need to complete the missing values in the table for different values of xx.

Table Setup:

For the equation y=5xy = 5^x, we calculate the values of yy based on the corresponding values of xx:

  • When x=2x = -2, y=52=125y = 5^{-2} = \frac{1}{25} (already given).
  • When x=1x = -1, y=51=15y = 5^{-1} = \frac{1}{5} (this is the missing value).
  • When x=0x = 0, y=50=1y = 5^0 = 1 (already given).
  • When x=1x = 1, y=51=5y = 5^1 = 5 (already given).
  • When x=2x = 2, y=52=25y = 5^2 = 25 (this is missing).
  • When x=3x = 3, y=53=125y = 5^3 = 125 (this is missing).

Completed Table:

x & y = 5^x \\ \hline -2 & \frac{1}{25} \\ -1 & \frac{1}{5} \\ 0 & 1 \\ 1 & 5 \\ 2 & 25 \\ 3 & 125 \\ \end{array}$$ Would you like to go over any step in more detail? --- Here are 5 related questions to expand your understanding: 1. How does the function $$y = 5^x$$ behave as $$x$$ increases or decreases? 2. What is the general form of exponential growth functions? 3. How do the values of $$y$$ change when $$x$$ is negative in an exponential function? 4. Can you plot the graph of $$y = 5^x$$ for the given values of $$x$$? 5. How would you solve for $$x$$ if you were given a specific value of $$y$$ in this function? **Tip:** Exponential functions grow very quickly when the base is greater than 1, and their graphs increase rapidly as $$x$$ becomes larger.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions

Formulas

y = 5^x

Theorems

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Suitable Grade Level

Grades 8-10