Question

Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 4)(0,4) and (3, 500)(3,500).

Answer 1

`4 = a b^0`

`a =4`

And we have this for the model:

`y = 4 b^x`

Now using the other point (3,500) we have this:

`500 = 4 b^3`

We can divide both sides by 4 and we got:

`125 = b^3`

And if we apply cubic root we got:

`b = (125)^(1/3)= 5`

So then the model would be:

`y = 4 (5)^x`

Explanation:

For this case we want to create an exponential function given by this general expression:

`y = a b^x`

And we have the following points (0.4) and (3.500). If we use the point (0,4) we have this:

`4 = a b^0`

`a =4`

And we have this for the model:

`y = 4 b^x`

Now using the other point (3,500) we have this:

`500 = 4 b^3`

We can divide both sides by 4 and we got:

`125 = b^3`

And if we apply cubic root we got:

`b = (125)^(1/3)= 5`

So then the model would be:

`y = 4 (5)^x`