Question

Which function models the data in the table?

Answer 1

(A) f(x) = 2 *
`4^(t)`

Explanation:

[] We can find our answer by plugging the x values into the functions as t and solving.

-. Using this method, starting with the A function, we find that the first function models the data and we do not need to test the others. I still have shown the work for the others as it is good to check your work.

[✓] f(x) = 2 *
`4^(t)`

(1, 8) }{}{}{ f(x) = 2 *
`4^(1)` = 2 * 4 = 8

(2, 32) }{}{}{ f(x) = 2 *
`4^(2)` = 2 * 16 = 32

(3, 128) }{}{}{ f(x) = 2 *
`4^(3)` = 2 * 64 = 128

-> This pattern continues

[✗] f(x) =
`4^(t)`

(1, 8) }{}{}{ f(x) =
`4^(1)` = 4 ≠ 8

-> This function does not model the data as it does not fulfil the first point

[✗] f(x) = 4 *
`2^(t)`

(1, 8) }{}{}{ f(x) = 4 *
`2^(1)` = 4 * 2 = 8

(2, 32) }{}{}{ f(x) = 4 *
`2^(2)` = 4 * 4 = 16 ≠ 32

-> This function only models (1, 8) but does not fully model the data

[✗] f(x) =
`8^(t)`

(1, 8) }{}{}{ f(x) =
`8^(1)` = 8

(2, 32) }{}{}{ f(x) =
`8^(2)` = 64 ≠ 32

-> This function only models (1, 8) but does not fully model the data

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather