The exponential function in the form y=abˣ that goes through points (0, 3) and (4, 48) is y=3(2ˣ).
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
In order to write the exponential function in the form y=abˣ, we need to find the value of the constants a and b, therefore, substitute the value of the two points in the general equation y=abˣ.
For the first point (0,3),
[tex]y=ab^x\\\\3=ab^0\\\\ 3 = a(1)\\\\a = 3[/tex]
As we know the value of 3 now, therefore, the function can be written as y=3bˣ, Now, substitute the value of the second point in this function to get the value of b.
[tex]y = 3b^x\\\\48 = 3b^4\\\\16= b^4\\\\\text{Taking log}\\\\\rm log_b16=4\\\\\dfrac{log\ 16}{log\ b} = 4\\\\\dfrac{log\ 16}{4} = {log\ b}\\\\\text{Taking anti log}\\\\b = 2[/tex]
Thus, the value of the a is 3 and the value of b is 2, substituting the values in the general equation of the exponential function. We will get the function as y=3(2ˣ).
Hence, the exponential function in the form y=abˣ that goes through points (0, 3) and (4, 48) is y=3(2ˣ).
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