hat is the slope of the secant line that intersects the graph of \( (x)=0.5^{-x} \) at \( x=1 \) and \( x=5 \) ?

To find the slope of the secant line that intersects the graph of \( f(x) = 0.5^{-x} \) at \( x = 1 \) and \( x = 5 \), we can use the formula for the slope of a secant line: \[ \text{Slope of secant line} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] Given: - \( f(x) = 0.5^{-x} \) - \( x_1 = 1 \) - \( x_2 = 5 \) Substitute the values into the formula to find the slope of the secant line. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(0.5^{-5}-0.5^{-1}\right)}{\left(5-1\right)}\) - step1: Remove the parentheses: \(\frac{0.5^{-5}-0.5^{-1}}{5-1}\) - step2: Convert the expressions: \(\frac{\left(\frac{1}{2}\right)^{-5}-0.5^{-1}}{5-1}\) - step3: Convert the expressions: \(\frac{\left(\frac{1}{2}\right)^{-5}-\left(\frac{1}{2}\right)^{-1}}{5-1}\) - step4: Subtract the numbers: \(\frac{30}{5-1}\) - step5: Subtract the numbers: \(\frac{30}{4}\) - step6: Reduce the fraction: \(\frac{15}{2}\) The slope of the secant line that intersects the graph of \( f(x) = 0.5^{-x} \) at \( x = 1 \) and \( x = 5 \) is \( \frac{15}{2} \) or \( 7.5 \).