Question

draw the graph of (f(x) = -\frac{1}{5} cdot (5)^{x-5} + 4)

Explanation:

Step1: Identify the horizontal asymptote

$$y = 4$$

Step2: Calculate the value at \(x = 5\)

$$f(5) = -\frac{1}{5} \cdot (5)^{0} + 4 = 3.8$$

Step3: Calculate the value at \(x = 6\)

$$f(6) = -\frac{1}{5} \cdot (5)^{1} + 4 = 3$$

Step4: Calculate the value at \(x = 7\)

$$f(7) = -\frac{1}{5} \cdot (5)^{2} + 4 = -1$$

Step5: Plot points and draw curve

Plot \((5, 3.8)\), \((6, 3)\), \((7, -1)\) with asymptote \(y = 4\).

Answer:

The graph of \(f(x) = -\frac{1}{5} \cdot (5)^{x-5} + 4\) is an exponential curve with a horizontal asymptote at \(y = 4\). It passes through the points \((4, 3.96)\), \((5, 3.8)\), \((6, 3)\), and \((7, -1)\), decreasing rapidly as \(x\) increases.