Question

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

Answer 1

Answer:

$a =5$

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:

$y= 5 (2)^x$

Step-by-step 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:

$y= 5 (2)^x$