Question

Use the table to answer the question.

This table presents the x and y values to identify the function that most accurately models the given dataset.
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)=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)=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)=92x−63
; f(−1)=−155

Answer 1

The data are geometric: each y is 3 times the previous (5,15,45,...). So the model is f(x)=5·3^x. At x=−1, f(−1)=5·3^(−1)=5/3 ≈ 1.6667.