Find an power function of the form y=ab^x whose graph passes through the points (4,4) and (16,8).

Hey, you do some.

To find a power function of the form y = ab^x that passes through the points (4,4) and (16,8), we can start by setting up a system of equations using the given points.

Let's consider the point (4,4). With x = 4 and y = 4, we have the equation:

4 = ab^4 -- Equation 1

Similarly, using the other point (16,8), with x = 16 and y = 8, we have:

8 = ab^16 -- Equation 2

We now have a system of two equations with two unknowns (a and b). We need to solve this system to find the values of a and b.

To eliminate the variable 'a' from the equations, we can divide Equation 2 by Equation 1:

(8/4) = ab^16 / ab^4
2 = b^12

To solve for b, we take the twelfth root of both sides:

b = ∛2

Now we substitute the value of b back into Equation 1 to find a:

4 = a (∛2)^4
4 = a * 2
a = 2

So the values of a and b are a = 2 and b = ∛2.

Finally, we can write the power function in the form y = ab^x using these values:

y = 2(∛2)^x

Therefore, the power function that passes through the points (4,4) and (16,8) is y = 2(∛2)^x.