Question

Evaluate the expression. $$\frac{(1-x)^{t}}{2} \text { when } x=0.09 \text { and } t=2$$

Short answer

The expression evaluates to 0.41405 when \(x\) is 0.09 and \(t\) is 2.

Step-by-step solution

Substitute given values.

The first step is to substitute the given values of \(x\) and \(t\) into the equation. Therefore, the equation \(\frac{(1-x)^{t}}{2}\) becomes \(\frac{(1-0.09)^{2}}{2}\).

Simplify the numerator.

Next, simplify the numerator of the fraction by subtracting 0.09 from 1, which equals to 0.91, and then raise it to the power of 2. So, \((1-0.09)^{2}\) equals to \((0.91)^{2}\), which equals 0.8281.

Divide by the denominator.

Lastly, divide the result by the denominator, which is 2. Therefore, \(\frac{0.8281}{2}\) equals to 0.41405.