which is the graph of f(x) = 100(0.7)^x?

Explanation:

Step1: Identify the form of the function

The function $f(x)=100(0.7)^x$ is an exponential - decay function of the form $y = a\cdot b^x$, where $a = 100$ and $b=0.7$ ($0 < b<1$).

Step2: Find the y - intercept

When $x = 0$, $f(0)=100(0.7)^0=100\times1 = 100$. So the y - intercept is $(0,100)$.

Step3: Evaluate the function at $x = 2$

When $x = 2$, $f(2)=100(0.7)^2=100\times0.49 = 49$.

Answer:

The graph with y - intercept $(0,100)$ and the point $(2,49)$ is the correct graph. (Based on the description of the points on the graphs in the problem, the first graph with $(0,100)$ and $(2,49)$ is the answer as the second graph has $(2,9)$ which is incorrect for the function $y = 100(0.7)^x$).