which function can be used to represent the graphed geometric sequence?\n○ (f(x)=80(\frac{1}{4})^{x - 1})\n○…

which function can be used to represent the graphed geometric sequence?\n○ (f(x)=80(\frac{1}{4})^{x - 1})\n○ (f(x)=320(\frac{1}{4})^{x - 1})\n○ (f(x)=80(4)^{x - 1})\n○ (f(x)=320(4)^{x - 1})

which function can be used to represent the graphed geometric sequence?\n○ (f(x)=80(\frac{1}{4})^{x - 1})\n○ (f(x)=320(\frac{1}{4})^{x - 1})\n○ (f(x)=80(4)^{x - 1})\n○ (f(x)=320(4)^{x - 1})

Answer

Explanation:

Step1: Recall geometric - sequence formula

The general formula for a geometric sequence is (f(x)=a\cdot r^{x - 1}), where (a) is the first - term and (r) is the common ratio.

Step2: Find the first - term (a)

From the graph, when (x = 1), (y=f(1)=80), so (a = 80).

Step3: Find the common ratio (r)

When (x = 2), (y = 20). Using the formula (f(x)=a\cdot r^{x - 1}), when (x = 2), (f(2)=a\cdot r^{2 - 1}=a\cdot r). Since (a = 80) and (f(2)=20), we have (80r=20), then (r=\frac{20}{80}=\frac{1}{4}).

Step4: Write the function

Substitute (a = 80) and (r=\frac{1}{4}) into the formula (f(x)=a\cdot r^{x - 1}), we get (f(x)=80(\frac{1}{4})^{x - 1}).

Answer:

(f(x)=80(\frac{1}{4})^{x - 1})