Question

graph these two functions on the graphing calculator: $y = 3x^2$ and $y = 3^x$ based on the graphs on your calculator, which function appears to grow faster? on the calculator, click on the graph of $y = 3x^2$ and trace to view the coordinates. when the x-coordinate is 4, what is the y-coordinate? on the calculator, click on the graph of $y = 3^x$ and trace to view the coordinates. when the x-coordinate is 4, what is the y-coordinate? when the x-coordinate is 4, which function has the greater value: $y = 3x^2$ or $y = 3^x$?

Explanation:

Sub - question 1: When \( x = 4 \), find \( y \) for \( y = 3x^{2} \)

Step 1: Substitute \( x = 4 \) into \( y = 3x^{2} \)

We know that to find the value of \( y \) when \( x = 4 \) in the function \( y=3x^{2}\), we substitute \( x = 4 \) into the function. So we get \( y = 3\times(4)^{2}\)

Step 2: Calculate the value

First, calculate \( 4^{2}=16\), then multiply by 3. So \( y=3\times16 = 48\)

Step 1: Substitute \( x = 4 \) into \( y = 3^{x} \)

To find the value of \( y \) when \( x = 4 \) in the function \( y = 3^{x}\), we substitute \( x=4\) into the function. So we get \( y=3^{4}\)

Step 2: Calculate the value

We know that \( 3^{4}=3\times3\times3\times3=81\)

Step 1: Recall the values

We found that when \( x = 4 \), for \( y = 3x^{2}\), \( y = 48\) and for \( y=3^{x}\), \( y = 81\)

Step 2: Compare the two values

Since \( 81>48\), the function \( y = 3^{x}\) has a greater value when \( x = 4 \)

Answer:

48

Sub - question 2: When \( x = 4 \), find \( y \) for \( y = 3^{x} \)