Question

which is the graph of $f(x) = 100(0.7)^x$? four graphs with coordinate planes and labeled points

Explanation:

Step1: Find the y-intercept

For the function \( f(x) = 100(0.7)^x \), when \( x = 0 \), \( f(0)=100(0.7)^0 = 100\times1 = 100 \). So the y - intercept is \( (0,100) \), which all graphs seem to have.

Step2: Calculate \( f(2) \)

Substitute \( x = 2 \) into the function: \( f(2)=100\times(0.7)^2=100\times0.49 = 49 \). So we need to find the graph that has the point \( (2,49) \).
Looking at the graphs, the third graph (top - right) has the point \( (2,49) \) along with \( (0,100) \) and the curve is a decreasing exponential curve (since the base \( 0.7<1 \)) which matches the behavior of \( f(x)=100(0.7)^x \).

Answer:

The top - right graph (the third graph in the top row) with points \( (0,100) \) and \( (2,49) \)