Question

Create an exponential equation from the points: (1, -6) & (2, -12)

(**Make sure you start it with f(x) and include parentheses)

Answer 1

The exponential equation is
`f(x)=-3(2)^x`

Step-by-step explanation:

The points are
`$(1,-6)$` and
`$(2,-12)$`

To determine the exponential equation, let us substitute the points in the exponential equation
`y=a(b)^x`

Substituting
`$(1,-6)$` in the equation
`y=a(b)^x`, we get,

`-6=a(b)^1`

`-6=ab`

`(-6)/(b) =a`

Thus, substituting
`(-6)/(b) =a` and
`$(2,-12)$` in
`y=a(b)^x`, we have,

`-12=(-6)/(b) (b)^2`

`-12=-6b`

`2=b`

Substituting
`b=2` in
`(-6)/(b) =a`, we get,

`(-6)/(2) =a\\`

`-3=a`

Hence, substituting the value of a and b in the exponential equation
`y=a(b)^x`, we have,

`y=-3(2)^x`

Thus, the exponential equation is
`f(x)=-3(2)^x`