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 \( x < 0 \).
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