Question

which is the graph of f(x) = 100(0.7)^x? two graphs are shown, first with (0,100) and (2,49), second with (0,100) and (2,9)

Explanation:

Step1: Analyze the function at x=0

For the function \( f(x) = 100(0.7)^x \), when \( x = 0 \), we use the property \( a^0=1 \) (where \( a
eq0 \)). So \( f(0)=100(0.7)^0 = 100\times1 = 100 \). Both graphs have the point (0, 100), so we need to check another point.

Step2: Analyze the function at x=2

Calculate \( f(2) \) using the function \( f(x)=100(0.7)^x \). Substitute \( x = 2 \): \( f(2)=100\times(0.7)^2 \). First, calculate \( (0.7)^2=0.7\times0.7 = 0.49 \). Then, \( 100\times0.49 = 49 \). So the point (2, 49) should be on the graph of \( f(x)=100(0.7)^x \).

Step3: Compare with the given graphs

The first graph has the point (2, 49) and the second graph has the point (2, 9). Since our calculation shows that at \( x = 2 \), \( f(x)=49 \), the correct graph is the first one (the one with the point (2, 49)).

Answer:

The graph with the points \((0, 100)\) and \((2, 49)\) (the upper - left graph among the two given graphs).