Type The Correct Answer In Each Box. Round Your Answers To One Decimal Place. Use The Function G ( X ) = 4 ( 0.6 ) X G(x) = 4(0.6)^x G ( X ) = 4 ( 0.6 ) X To Complete The Table And Find The Y Y Y -intercept. \[ \begin{tabular}{|c|c|} \hline X$ & G ( X ) G(x) G ( X ) \ \hline -10 & 4.0

Exploring the Function $g(x) = 4(0.6)^x$

Understanding the Function

The given function is $g(x) = 4(0.6)^x$. This is an exponential function, where the base is 0.6 and the coefficient is 4. The function is defined for all real values of x.

Rounding Answers to One Decimal Place

In this problem, we are asked to round our answers to one decimal place. This means that we will need to calculate the values of $g(x)$ for each value of x and then round the results to one decimal place.

Completing the Table

To complete the table, we will need to calculate the values of $g(x)$ for each value of x. We will use the function $g(x) = 4(0.6)^x$ to calculate these values.

Finding the $y$-intercept

The $y$-intercept of a function is the value of the function when x is equal to 0. To find the $y$-intercept of the function $g(x) = 4(0.6)^x$, we will substitute x = 0 into the function.

g(0) = 4(0.6)^0 g(0) = 4(1) g(0) = 4

Therefore, the $y$-intercept of the function $g(x) = 4(0.6)^x$ is 4.

Discussion

The function $g(x) = 4(0.6)^x$ is an exponential function that decreases as x increases. The function has a $y$-intercept of 4, which means that the function passes through the point (0, 4) on the coordinate plane.

Conclusion

In this problem, we used the function $g(x) = 4(0.6)^x$ to complete a table of values and find the $y$-intercept. We calculated the values of $g(x)$ for each value of x and rounded the results to one decimal place. We also found the $y$-intercept of the function by substituting x = 0 into the function.

Key Takeaways

• The function $g(x) = 4(0.6)^x$ is an exponential function that decreases as x increases.
• The function has a $y$-intercept of 4.
• To find the $y$-intercept of an exponential function, substitute x = 0 into the function.

Further Exploration

• Use the function $g(x) = 4(0.6)^x$ to complete a table of values for x = -20 to x = 20.
• Find the $y$-intercept of the function $g(x) = 4(0.8)^x$.
• Compare the graphs of the functions $g(x) = 4(0.6)^x$ and $g(x) = 4(0.8)^x$.
  Q&A: Exploring the Function $g(x) = 4(0.6)^x$

Frequently Asked Questions

We have received many questions about the function $g(x) = 4(0.6)^x$. Here are some of the most frequently asked questions and their answers.

Q: What is the domain of the function $g(x) = 4(0.6)^x$?

A: The domain of the function $g(x) = 4(0.6)^x$ is all real numbers. This means that the function is defined for all values of x.

Q: What is the range of the function $g(x) = 4(0.6)^x$?

A: The range of the function $g(x) = 4(0.6)^x$ is all positive real numbers. This means that the function will always produce a positive value.

Q: How do I find the $y$-intercept of the function $g(x) = 4(0.6)^x$?

A: To find the $y$-intercept of the function $g(x) = 4(0.6)^x$, substitute x = 0 into the function. This will give you the value of the function at x = 0.

Q: How do I complete a table of values for the function $g(x) = 4(0.6)^x$?

A: To complete a table of values for the function $g(x) = 4(0.6)^x$, substitute different values of x into the function and calculate the corresponding values of $g(x)$.

Q: What is the effect of increasing the value of x on the function $g(x) = 4(0.6)^x$?

A: Increasing the value of x will decrease the value of the function $g(x) = 4(0.6)^x$. This is because the function is an exponential function with a base less than 1.

Q: How do I compare the graphs of two exponential functions?

A: To compare the graphs of two exponential functions, look at the base and the coefficient of each function. The function with the smaller base will have a steeper graph, while the function with the larger coefficient will have a taller graph.

Q: What is the significance of the $y$-intercept of an exponential function?

A: The $y$-intercept of an exponential function is the value of the function at x = 0. This is an important point on the graph of the function, as it represents the starting point of the function.

Q: How do I use the function $g(x) = 4(0.6)^x$ in real-world applications?

A: The function $g(x) = 4(0.6)^x$ can be used to model real-world situations where a quantity decreases exponentially over time. For example, it can be used to model the decay of a radioactive substance or the decrease in population of a species over time.

Conclusion

We hope that this Q&A article has been helpful in answering your questions about the function $g(x) = 4(0.6)^x$. If you have any further questions, please don't hesitate to ask.

Key Takeaways

• The domain of the function $g(x) = 4(0.6)^x$ is all real numbers.
• The range of the function $g(x) = 4(0.6)^x$ is all positive real numbers.
• The $y$-intercept of the function $g(x) = 4(0.6)^x$ is 4.
• Increasing the value of x will decrease the value of the function $g(x) = 4(0.6)^x$.
• The function $g(x) = 4(0.6)^x$ can be used to model real-world situations where a quantity decreases exponentially over time.

Further Exploration

• Use the function $g(x) = 4(0.6)^x$ to model the decay of a radioactive substance.
• Compare the graphs of the functions $g(x) = 4(0.6)^x$ and $g(x) = 4(0.8)^x$.
• Find the $y$-intercept of the function $g(x) = 4(0.8)^x$.