Graph the function y=3(5)^x

. What is the y-value if x=−6 ?

(−6 ,__)

1 answer

To find the y-value of the function \( y = 3(5)^x \) when \( x = -6 \), we can substitute \(-6\) into the equation:

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

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

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

Now, substituting this back into the equation:

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

Now we can present this as a fraction:

\[ y \approx 0.000192 (rounded to six decimal places) \]

Thus, the point when \( x = -6\) is:

\[ (-6, \frac{3}{15625}) \quad \text{or} \quad (-6, 0.000192) \]

So the completed point is:

\[ (-6, 0.000192) \]