Question
Graph the function y=3(5)x
. What is the y-value if x=−6
?(1 point)
(−6
,
)
. What is the y-value if x=−6
?(1 point)
(−6
,
)
Answers
Answered by
GPT-4o mini
To evaluate the function \( y = 3(5)^x \) at \( x = -6 \), we can substitute \(-6\) into the equation:
\[
y = 3(5)^{-6}
\]
Now, let's calculate \( (5)^{-6} \):
\[
(5)^{-6} = \frac{1}{(5)^6}
\]
Next, we need to calculate \( (5)^6 \):
\[
(5)^6 = 15625
\]
Thus, we have:
\[
(5)^{-6} = \frac{1}{15625}
\]
Now substitute this back into the equation for \( y \):
\[
y = 3 \times \frac{1}{15625} = \frac{3}{15625}
\]
So, the y-value when \( x = -6 \) is:
\[
\left(-6, \frac{3}{15625}\right)
\]
This corresponds to approximately:
\[
-6, 0.000192
\] (if needed in decimal form).
Therefore, the answer is \( (-6, \frac{3}{15625}) \).
\[
y = 3(5)^{-6}
\]
Now, let's calculate \( (5)^{-6} \):
\[
(5)^{-6} = \frac{1}{(5)^6}
\]
Next, we need to calculate \( (5)^6 \):
\[
(5)^6 = 15625
\]
Thus, we have:
\[
(5)^{-6} = \frac{1}{15625}
\]
Now substitute this back into the equation for \( y \):
\[
y = 3 \times \frac{1}{15625} = \frac{3}{15625}
\]
So, the y-value when \( x = -6 \) is:
\[
\left(-6, \frac{3}{15625}\right)
\]
This corresponds to approximately:
\[
-6, 0.000192
\] (if needed in decimal form).
Therefore, the answer is \( (-6, \frac{3}{15625}) \).
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