Question

Find the exponential function passing through points (-1,4/3) and (3,108)

Answer 1

its 152 i know cause i just did this....

Step-by-step explanation:

Answer 2

An exponential function is in the general form
`\mathrm{y}=\mathrm{a}(\mathrm{b})^{\mathrm{x}}`

Step-by-step explanation:

(x,y) = (-1,4/3) and (x,y)= (3,108) are the given functions

Therefore,

`(4)/(3)=a(b)^(-1)=(a)/(b)`

`(4)/(3)=(a)/(b)` - eq(1)

`108=a(b)^(3)=a b^(3)=108-e q(2)`

Multiply both sides of the first equation by b to find that

`(4)/(3) b=a`

Substituting in eq-2 we get

`(4)/(3) b^(4)=108`

`b^(4)=81`

`\mathrm{b}=\pm 3`

`\mathrm{b}=+3, \text { then } 108=\mathrm{a}(3)^(3)`

which gives a = 4,

henceforth the equation becomes as
`\mathrm{y}=4(3)^{\mathrm{x}}`

`\mathrm{b}=-3 \text { then } 108=\mathrm{a}(-3)^(3)`

which gives a = -4,

henceforth the equation becomes as y =
`-4(-3)^(x)`

However! In an exponential function, b>0, otherwise many issues arise when trying to graph the function.

The only valid function is
`4(3)^(x)`