Question

Exponential equation. Picture is attached.

Answer 1

`y=106.656*(0.816)^x`

Explanation:

The exponential equation will be of the form:

`y=ba^x.`

Now from the information give we have two points:

at
`x=3,`
`y=58.`

at
`x=10,`
`y=14.`

Thus we have two equations

`(1).58=ba^3,`

`(2).14=ba^(10).`

From equation
`(1)` we solve for
`b`:

`b=(58)/(a^3),`

and put this value into equation
`(2)` and we get:

`14=(58)/(a^3)*a^(10)=58a^7,`

and solve for
`a:`

`a=\sqrt[7]{(14)/(58) }=0.8162.`

`\boxed{a=0.816.}`

We now put this value into equation (1) and solve for
`b`:

`\boxed{b=(58)/((0.8162)^3) =106.656.}`.

With values of
`a` and
`b` in hand, we have our exponential function:

`\boxed{y=106.656*(0.816)^x.}`