Question

Write an exponential function for the table. X 1 2 3 4 y 6 18 54 162 please l need help​

Answer 1

y = 2
`(3)^(x)`

Explanation:

the standard form of an exponential function is

y = a
`b^(x)`

to find a and b use ordered pairs from the table

using (1, 6 )

6 = a
`b^(1)` , that is

6 = ab → (1)

using (3, 54 )

54 = ab³ → (2)

divide (2) by (1) on both sides

`(54)/(6)` =
`(ab^3)/(ab)` , that is

b² = 9 ( take square root of both sides )

b =
`√(9)` = 3

substitute b = 3 into (1) and solve for a

6 = 3a ( divide both sides b 3 )

2 = a

then the exponential function for the table is

y = 2
`(3)^(x)`