which is the best description of the graph of the function ( f(x)=60(\frac{1}{3})^{x} )?\nthe graph has an…

which is the best description of the graph of the function ( f(x)=60(\frac{1}{3})^{x} )?\nthe graph has an initial value of 20, and each successive term is determined by subtracting ( \frac{1}{3} ).\nthe graph has an initial value of 20, and each successive term is determined by multiplying by ( \frac{1}{3} ).\nthe graph has an initial value of 60, and each successive term is determined by subtracting ( \frac{1}{3} ).\nthe graph has an initial value of 60, and each successive term is determined by multiplying by ( \frac{1}{3} ).

which is the best description of the graph of the function ( f(x)=60(\frac{1}{3})^{x} )?\nthe graph has an initial value of 20, and each successive term is determined by subtracting ( \frac{1}{3} ).\nthe graph has an initial value of 20, and each successive term is determined by multiplying by ( \frac{1}{3} ).\nthe graph has an initial value of 60, and each successive term is determined by subtracting ( \frac{1}{3} ).\nthe graph has an initial value of 60, and each successive term is determined by multiplying by ( \frac{1}{3} ).

Answer

Explanation:

Step1: Find the initial value

For the exponential function (y = a\cdot b^{x}), when (x = 0), (y=a). For the function (f(x)=60(\frac{1}{3})^{x}), when (x = 0), (f(0)=60\times(\frac{1}{3})^{0}). Since (a^{0}=1) ((a\neq0)), then (f(0)=60\times1 = 60). So the initial value is (60).

Step2: Analyze the relationship between successive terms

Let (x=n) and (x=n + 1). (f(n)=60\times(\frac{1}{3})^{n}), (f(n + 1)=60\times(\frac{1}{3})^{n+1}). We know that (\frac{f(n + 1)}{f(n)}=\frac{60\times(\frac{1}{3})^{n+1}}{60\times(\frac{1}{3})^{n}}). Using the rule (a^{m}\div a^{n}=a^{m - n}), (\frac{f(n + 1)}{f(n)}=\frac{1}{3}). So each successive term is obtained by multiplying the previous term by (\frac{1}{3}).

Answer:

The graph has an initial value of (60), and each successive term is determined by multiplying by (\frac{1}{3}).