Question

Use the graph to write an explicit function to represent the data and determine how much money Amy earned in week 5.

Answer 1

Answer:

C

Step-by-step explanation:

Answer 2

Answer:

3rd option

$f(n)=5(3)^{n-1}$

$f(5)=405$

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 $f(n)=a_1 \cdot r^{n-1}$

where $a_1$ is the first term and r is the common ration.

So we have

$f(n)=5 \cdot (3)^{n-1}$.

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

$f(5)=5 \cdot (3)^{5-1}$

Simplifying:

$f(5)=5 \cdot 3^4$

$f(5)=5 \cdot 81$

$f(5)=405$