Question

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

Explanation:

Step1: Identify initial point

When $x=0$, $f(0)=100(0.7)^0=100$. So the graph passes through $(0,100)$, which all options have.

Step2: Calculate f(2)

Substitute $x=2$ into the function:
$f(2)=100(0.7)^2=100\times0.49=49$
This means the graph must pass through $(2,49)$.

Step3: Match with options

Compare the calculated point $(2,49)$ to the points shown in each graph.

Answer:

The fourth graph (with the point $(2,49)$) is the correct graph of $f(x)=100(0.7)^x$.