Question

Write an exponential function y = abx for a graph that includes (1, 15) and (0, 6).

Answer 1

see explanation

Explanation:

Obtain the exponential function by substituting the given points into the equation.

Equation in form

y = a
`b^(x)`

Using (0, 6), then

6 = a
`b^(0)` = a ⇒ a = 6

Using (1, 15), then

15 = 6
`b^(1)` = 6b ( divide both sides by 6 )

`(15)/(6)` = b, hence

b =
`(5)/(2)`

Exponential equation is y = 6
`((5)/(2)) ^(x)`

Answer 2

`y = 6(2.5)^x`

Explanation:

`y = ab^x`

Use (0, 6) and solve for a:

`6 = ab^0`

`6 = a * 1`

`a = 6`

Use a = 6 and (1, 15) and solve for b.

`15 = 6b^1`

`15 = 6b`

`6 = 2.5`

`y = 6(2.5)^x`