Question

Which function is graphed below?

A) y=1/3(3)^x
B) y=3(1/3)^x
C)y=(1/2)^x+2
D) y=(2)^x-1

Answer 1

B) y=3(1/3)^x

Explanation:

Based on the graph, y intercept = 3

So you can plug in x =0 in each functions given in the options to see which one has y-intercept = 3

y= 3 (1/3)^x ; when x = 0, y = 3 * 3^0 = 3 * 1 = 3

Answer 2

The correct option is B)
`y=3((1)/(3))^(x)`

Explanation:

Consider the provided graph:

The general formula for equation of exponential decay is:
`y=ab^(x)` where
`b<1`

The graph of exponential decay
`y=ab^(x)` where
`b<1` as shown in figure 1:

From the figure 1, it is clear that a represents the y intercept and the coordinates are (0,a).

Now, consider the provided Graph:

The y intercept is (0,3)

Therefore, the value of a must be 3.

Now, consider the provided options, only option B) has the value of a = 3.

Therefore, the correct option is: B)
`y=3((1)/(3))^(x)` .