Question

Graph the function y=3\left(5\right)^{x}. What is the y value if x=-6?

Answer 1

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 need to calculate \( (5)^{-6} \):

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

Next, we can calculate \( (5)^6 \):

\[
5^6 = 15625
\]

Thus,

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

Now substitute this back into the equation for \( y \):

\[
y = 3 \left( \frac{1}{15625} \right) = \frac{3}{15625}
\]

Calculating the fraction gives us:

\[
y = 0.000192
\]

So, when \( x = -6 \), the y-value is approximately \( 0.000192 \).

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

\[
\frac{3}{15625} \approx 0.000192
\]