1. **State the problem:** We are given two points on the graph of an exponential function: (1, 24) and (2, 144). We need to find the function of the form $$f(x) = a b^x$$ where $a$ and $b$ are constants. 2. **Formula and rules:** The general form of an exponential function is $$f(x) = a b^x$$ where $a$ is the initial value (when $x=0$) and $b$ is the base or growth factor. 3. **Use the points to form equations:** - Using point (1, 24): $$f(1) = a b^1 = a b = 24$$ - Using point (2, 144): $$f(2) = a b^2 = 144$$ 4. **Divide the second equation by the first to eliminate $a$:** $$\frac{a b^2}{a b} = \frac{144}{24}$$ $$\cancel{a} b^{2-1} / \cancel{a} = 6$$ $$b = 6$$ 5. **Substitute $b=6$ back into the first equation:** $$a \times 6 = 24$$ $$a = \frac{24}{6}$$ $$a = 4$$ 6. **Write the function:** $$f(x) = 4 \times 6^x$$ 7. **Check the options:** The function matches option: $$f(x) = 4(6)^x$$ **Final answer:** $$f(x) = 4(6)^x$$