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

Answer:

$4 = a b^0$

$a =4$

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:

$y = 4 (5)^x$

Step-by-step 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:

$y = 4 (5)^x$