Question

Write an exponential function in the form y=ab x that goes through points ( 0 , 6 ) and (5,1458).

Answer 1

With
`y=ab^x`, we can convert each point given into an equation:

(0,6) becomes
`6=a\cdot b^0`.

Since
`b^0=1`, this equation becomes
`6=a\cdot 1` or
`6=a`.

We now have
`y=6\cdot b^x` and if we combine that with (5,1458), we have

`1458 = 6\cdot b^5`

which we can solve for b by dividing both sides by 6 and then taking the 5th root of both sides:

`1458 = 6\cdot b^5`

`243 = b^5`

`\sqrt[5]{243} =b`

`3=b`

So now we have the function:
`y = 6 \cdot 3^x`.