Respuesta :

Answer:

[tex]y = 16*2^{x}[/tex]

Step-by-step explanation:

We want an exponential function in the following format:

[tex]y = ab^{x}[/tex]

Goes through the point (0,16).

This means that when [tex]x = 0, y = 16[/tex]

So

[tex]y = ab^{x}[/tex]

[tex]16 = ab^{0}[/tex]

Since [tex]b^{0} = 1[/tex]

[tex]a = 16[/tex]

So

[tex]y = 16b^{x}[/tex]

Goes through the point (7,2048).

This means that when [tex]x = 7, y = 2048[/tex]

Then

[tex]y = 16b^{x}[/tex]

[tex]2048 = 16b^{7}[/tex]

[tex]b^{7} = \frac{2048}{16}[/tex]

[tex]b^{7} = 128[/tex]

[tex]b = \sqrt[7]{128}[/tex]

[tex]b = 2[/tex]

So the function is:

[tex]y = 16*2^{x}[/tex]

shallomisaiah19

Answer:

[tex]y = 16*2^{x}[/tex]

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:

[tex]y= ab^x[/tex]

And using the first point given we have:

[tex]16 = a b^0 a = 16[/tex]

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

[tex]2048 = 16 b^7[/tex]

We can divide 16 in both sides and we got

[tex]128=b^7[/tex]

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

[tex](128)^{1/7} = b b = 2[/tex]

And then our model would be given:

[tex]y = 16*2^{x}[/tex]

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