Graph The Function F ( X ) = 16 ( 1.87 ) X F(x)=16(1.87)^x F ( X ) = 16 ( 1.87 ) X . Does This Function Show Growth Or Decay? What Is The Equation Of The Asymptote?A. Growth; Y = − 16 Y=-16 Y = − 16 B. Growth; Y = 0 Y=0 Y = 0 C. Decay; Y = − 16 Y=-16 Y = − 16 D. Decay; Y = 0 Y=0 Y = 0

Graphing the Function $f(x)=16(1.87)^x$ and Analyzing Growth or Decay

In this article, we will explore the function $f(x)=16(1.87)^x$ and analyze its behavior, specifically whether it shows growth or decay. We will also determine the equation of the asymptote for this function.

Understanding the Function

The given function is an exponential function of the form $f(x)=ab^x$, where $a$ and $b$ are constants. In this case, $a=16$ and $b=1.87$. The value of $b$ is greater than 1, which indicates that the function will exhibit growth.

Graphing the Function

To graph the function, we can use a graphing calculator or software. However, we can also analyze the function's behavior by examining its components. The function $f(x)=16(1.87)^x$ can be rewritten as $f(x)=16e^{x\ln(1.87)}$, where $e$ is the base of the natural logarithm and $\ln$ is the natural logarithm function.

Analyzing Growth or Decay

As mentioned earlier, the value of $b$ is greater than 1, which indicates that the function will exhibit growth. This means that as $x$ increases, the value of $f(x)$ will also increase.

Determining the Equation of the Asymptote

The equation of the asymptote for an exponential function of the form $f(x)=ab^x$ is given by $y=0$. This is because as $x$ approaches negative infinity, the value of $f(x)$ approaches 0.

Conclusion

In conclusion, the function $f(x)=16(1.87)^x$ shows growth, and the equation of the asymptote is $y=0$. This means that as $x$ increases, the value of $f(x)$ will also increase, and as $x$ approaches negative infinity, the value of $f(x)$ will approach 0.

Answer

Based on our analysis, the correct answer is:

• Growth: Yes
• Equation of the asymptote: y=0

Final Answer

The final answer is B. Growth; $y=0$.
Q&A: Graphing the Function $f(x)=16(1.87)^x$ and Analyzing Growth or Decay

In our previous article, we explored the function $f(x)=16(1.87)^x$ and analyzed its behavior, specifically whether it shows growth or decay. We also determined the equation of the asymptote for this function. In this article, we will answer some frequently asked questions related to graphing the function and analyzing growth or decay.

Q: What is the base of the exponential function $f(x)=16(1.87)^x$?

A: The base of the exponential function $f(x)=16(1.87)^x$ is 1.87.

Q: Is the function $f(x)=16(1.87)^x$ an increasing or decreasing function?

A: The function $f(x)=16(1.87)^x$ is an increasing function, as the value of $b$ is greater than 1.

Q: What is the equation of the asymptote for the function $f(x)=16(1.87)^x$?

A: The equation of the asymptote for the function $f(x)=16(1.87)^x$ is $y=0$.

Q: How does the function $f(x)=16(1.87)^x$ behave as $x$ approaches negative infinity?

A: As $x$ approaches negative infinity, the value of $f(x)$ approaches 0.

Q: Can the function $f(x)=16(1.87)^x$ be rewritten in a different form?

A: Yes, the function $f(x)=16(1.87)^x$ can be rewritten as $f(x)=16e^{x\ln(1.87)}$, where $e$ is the base of the natural logarithm and $\ln$ is the natural logarithm function.

Q: What is the value of $a$ in the function $f(x)=16(1.87)^x$?

A: The value of $a$ in the function $f(x)=16(1.87)^x$ is 16.

Q: Is the function $f(x)=16(1.87)^x$ an example of exponential growth or decay?

A: The function $f(x)=16(1.87)^x$ is an example of exponential growth, as the value of $b$ is greater than 1.

Q: How can the function $f(x)=16(1.87)^x$ be graphed?

A: The function $f(x)=16(1.87)^x$ can be graphed using a graphing calculator or software.

Conclusion

In conclusion, we have answered some frequently asked questions related to graphing the function $f(x)=16(1.87)^x$ and analyzing growth or decay. We hope that this article has provided valuable information and insights for readers.

Final Answer

The final answer is B. Growth; $y=0$.