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

When $x = 0$, $f(0)=60\times(\frac{1}{3})^0$. Since any non - zero number to the power of 0 is 1, $f(0)=60\times1 = 60$.

Step2: Analyze the common ratio

For an exponential function of the form $y = a\times b^x$, the common ratio between consecutive terms is $b$. Here, the function is $f(x)=60\times(\frac{1}{3})^x$, so the common ratio between consecutive terms is $\frac{1}{3}$. That means each successive term is determined 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 $\frac{1}{3}$.