Question

Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 5) and (8, 1280)

Answer 1

`a =5`

Now we can use the info from the second point and we have:

`1280 = 5 b^8`

We can divide 5 in both sides and we got:

`256 = b^8`

And using an exponent 1/8 in both sides we got:

`(256)^(1/8) = b`

`b = 2`

And then our model would be given:

`y= 5 (2)^x`

Explanation:

For this case we have two points given (0,5) and (8,1280). And we want to find a function given by this general expression:

`y= ab^x`

And using the first point given we have:

`5 = a b^0`

`a =5`

Now we can use the info from the second point and we have:

`1280 = 5 b^8`

We can divide 5 in both sides and we got:

`256 = b^8`

And using an exponent 1/8 in both sides we got:

`(256)^(1/8) = b`

`b = 2`

And then our model would be given:

`y= 5 (2)^x`