Question

Graph the function y = 3(5)^x. If the X value is -6, what is the Y value? Show your anseer with a graph point.

Answer 1

To evaluate the function \( y = 3(5)^x \) at \( x = -6 \), we can substitute \(-6\) into the equation.

\[
y = 3(5)^{-6}
\]

Now, we can compute \( (5)^{-6} \):

\[
(5)^{-6} = \frac{1}{(5)^6}
\]

Calculating \( (5)^6 \):

\[
(5)^6 = 15625
\]

So,

\[
(5)^{-6} = \frac{1}{15625}
\]

Now, substituting this into the equation for \( y \):

\[
y = 3 \times \frac{1}{15625} = \frac{3}{15625}
\]

Thus, the value of \( y \) when \( x = -6 \) is:

\[
y = \frac{3}{15625}
\]

Now, let's plot this point on a graph.

### Coordinates of the point:
- \( x = -6 \)
- \( y = \frac{3}{15625} \approx 0.000192 \)

### Graph Point
The point is:

\[
(-6, 0.000192)
\]

### Graph Representation
To visually represent this on a graph, you would draw the x-axis and y-axis, and mark the point at approximately \( ( -6, 0.000192 ) \), which is very close to the x-axis due to its small y value.

### Note:
Creating an actual graph requires graphing software or graph paper where you can mark this point accurately. You can also sketch the general shape of the function \( y = 3(5)^x \) which will show exponential growth for \( x \geq 0 \) and decline towards zero for \( x < 0 \).