Use the graph to write an explicit function to represent the data and determine how much money amy earned in week 5.
graph with x axis labeled number of weeks and ranges from zero to seven, y axis labeled money earned, in dollars, and ranges from zero to one hundred eighty with points at one comma five, two comma fifteen, three comma forty five and four comma one hundred thirty five
f(n) = 5(3)^n + 1; f(5) = 3,645
f(n) = 5(3)^n; f(5) = 1,215
f(n) = 5(3)^n − 1; f(5) = 405
f(n) = (3)^n − 1; f(5) = 81

3rd option

Step-by-step explanation:

So we are given the following points:

(1,5)

(2,15)

(3,45)

(4,135)

This is a geometric sequence because there is a common ratio, 3. That is you can keep multiply 3 to a previous y-coordinate to get the next y-coordinate.

The formula for a geometric sequence is

where is the first term and r is the common ration.

So we have

.

If you want to know the fifth term, just plug in 5:

Simplifying:

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.