Question

Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function.

x: 0, 1, 2, 3, 4
f(x): 14, 12.6, 11.34, 10.206, 9.185

A) Exponential; y= 14(0.10)^x
B) Linear; y= -1.2024x + 13.871
C) Exponential; y= 14(0.90)^x
D) Linear; 18.871x - 1.2024

Please explain answer, I need to make corrections on my quiz. Please, please help.

Answer 1

The answer is C, the function is not following constant change, so not linear, and if it was .1^x, then it would be 1.4 instead of 12.6. So C is correct.

Answer 2

C) Exponential; y= 14(0.90)^x

Explanation:

Given is a table in

x 0 1 2 3 4

f(x) 14 12.6 11.34 10.206 9.185

On observing the pattern we find that whenever x increases by 1, y decreases.

But the decrease is not constant hence relationship cannot be linear for x and y.

The change of y follows some pattern as a geometric sequence with common ratio as 0.9

I term is for x =0 and then x increases by 1 unit.

Hence when x=x, we have

`y = 14(0.9)^(x)`

Option C is right answer.