Questions: If (g(x)=left(frac15right)^x), find (g(2.95)) (g(2.95)=)

If (g(x)=left(frac15right)^x), find (g(2.95)) (g(2.95)=)
Transcript text: If $g(x)=\left(\frac{1}{5}\right)^{x}$, find $g(2.95)$ \[ g(2.95)= \] $\square$
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Solution

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Solution Steps

To find \( g(2.95) \) for the function \( g(x) = \left(\frac{1}{5}\right)^{x} \), we need to evaluate the expression by substituting \( x = 2.95 \) into the function. This involves calculating the power of a fraction, which can be done using Python's exponentiation capabilities.

Step 1: Define the Function

We start with the function defined as \( g(x) = \left(\frac{1}{5}\right)^{x} \).

Step 2: Substitute the Value

To find \( g(2.95) \), we substitute \( x = 2.95 \) into the function: \[ g(2.95) = \left(\frac{1}{5}\right)^{2.95} \]

Step 3: Calculate the Result

Evaluating the expression gives us: \[ g(2.95) \approx 0.008670387093874944 \] Rounding this result to the nearest thousandth, we find: \[ g(2.95) \approx 0.009 \]

Final Answer

\(\boxed{0.009}\)

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