Question

x-Values y-Values
0 5
1 15
2 45
3 135
4 405
Select the function that best models the data and determine the value of the function at x=−1
.

(1 point)
Responses

f(x)=5⋅3x
; f(−1)=53
f of x is equal to 5 times 3 to the x th power; f of negative 1 is equal to 5 thirds

f(x)=41.43x2−73.71x+19.86
; f(−1)=135
f of x is equal to 41 point 4 3 x squared minus 73 point 7 1 x plus 19 point 8 6; f of negative 1 is equal to 135

f(x)=2.23⋅(1.40)x
; f(−1)=1.59
f of x is equal to 2 point 2 3 times 1 point 4 0 to the x th power ; f of negative 1 is equal to 1 point 5 9

f(x)=92x−63
; f(−1)=−155
f of x is equal to 92 x minus 63; f of negative 1 is equal to negative 155
Question 2

Answer 1

To find the function that best models the given data, we can analyze the relationship between the x-values and the y-values given in your table:

```
x y
0 5
1 15
2 45
3 135
4 405
```

We notice a pattern in the y-values that suggests a relationship based on powers of 3:

- For x = 0, y = 5, which is basically \(5 \cdot 3^0 = 5\)
- For x = 1, y = 5 \cdot 3^1 = 15
- For x = 2, y = 5 \cdot 3^2 = 45
- For x = 3, y = 5 \cdot 3^3 = 135
- For x = 4, y = 5 \cdot 3^4 = 405

This indicates that the function \(f(x) = 5 \cdot 3^x\) is indeed a good fit for the data provided.

Now let's calculate \(f(-1)\):

\[
f(-1) = 5 \cdot 3^{-1} = 5 \cdot \frac{1}{3} = \frac{5}{3}
\]

Thus, from the options:

- **f(x) = 5⋅3^x; f(−1)=53**

This is the correct choice. Therefore:

**f(−1) = \frac{5}{3}** or **5/3**.