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) g(2.95) for the function g(x)=(15)x g(x) = \left(\frac{1}{5}\right)^{x} , we need to evaluate the expression by substituting x=2.95 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)=(15)x g(x) = \left(\frac{1}{5}\right)^{x} .

Step 2: Substitute the Value

To find g(2.95) g(2.95) , we substitute x=2.95 x = 2.95 into the function: g(2.95)=(15)2.95 g(2.95) = \left(\frac{1}{5}\right)^{2.95}

Step 3: Calculate the Result

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

Final Answer

0.009\boxed{0.009}

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