To find the \( y \)-value of the function \( y = 3(5)^x \) when \( x = -6 \), we can substitute \(-6\) into the function.
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Calculate \( (5)^{-6} \): \[ (5)^{-6} = \frac{1}{(5)^6} \] Now calculate \( (5)^6 \): \[ (5)^6 = 15625 \] Therefore, \[ (5)^{-6} = \frac{1}{15625} \]
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Substitute back into the function: \[ y = 3(5)^{-6} = 3 \cdot \frac{1}{15625} = \frac{3}{15625} \]
So, the \( y \)-value when \( x = -6 \) is: \[ y = \frac{3}{15625} \]
If you need this value as a decimal, you can compute: \[ \frac{3}{15625} \approx 0.000192 \]
Thus, the \( y \)-value when \( x = -6 \) is approximately \( 0.000192 \) or exactly \( \frac{3}{15625} \).