Final answer:
To write an exponential function in the form y = abˣ that goes through (0, 16) and (6, 1024), the values of a and b can be determined by substituting the given coordinates into the equation. After finding the values of a = 16 and b = 2, the exponential function y = 16(2ˣ) can be obtained.
Step-by-step explanation:
To write an exponential function in the form y=abˣ that goes through (0, 16) and (6, 1024), we need to find the values of a and b. Let's use the point (0, 16) to determine the value of a. Plugging in x=0 and y=16 into the equation, we get 16 = ab⁰ = a.
Now let's use the point (6, 1024) to determine the value of b. Plugging in x=6 and y=1024 into the equation, we get 1024 = 16b⁶. Dividing both sides by 16, we get 64 = b⁶. Taking the 6th root of both sides, we get b = 2. Therefore, the exponential function that goes through (0, 16) and (6, 1024) is y = 16(2ˣ).