Question

Write an exponential function in the form y=ab^xy=ab x

Answer 1

Answer:

$y = 16*2^{x}$

Step-by-step explanation:

We want an exponential function in the following format:

$y = ab^{x}$

Goes through the point (0,16).

This means that when $x = 0, y = 16$

So

$y = ab^{x}$

$16 = ab^{0}$

Since $b^{0} = 1$

$a = 16$

So

$y = 16b^{x}$

Goes through the point (7,2048).

This means that when $x = 7, y = 2048$

Then

$y = 16b^{x}$

$2048 = 16b^{7}$

$b^{7} = \frac{2048}{16}$

$b^{7} = 128$

$b = \sqrt[7]{128}$

$b = 2$

So the function is:

$y = 16*2^{x}$

Answer 2

Answer:

$y = 16*2^{x}$

Step-by-step explanation:

For this case we have two points given (0,16) and (7,2048). And we want to find a function given by this general expression:

$y= ab^x$

And using the first point given we have:

$16 = a b^0 a = 16$

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

$2048 = 16 b^7$

We can divide 16 in both sides and we got

$128=b^7$

And using an exponent 1/7 in both sides we got:

$(128)^{1/7} = b b = 2$

And then our model would be given:

$y = 16*2^{x}$