Write an exponential function in the form y=ab^(x) that goes through the points (0,16) and (2,784). Answer:

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Write an exponential function in the form  y=ab^(x) that goes through the points  (0,16) and  (2,784). Answer:

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Find 'a' value: Given points: (0, 16) and (2, 784), we need to find the exponential function of the form y = ab^x. We will use the first point to find the value of 'a' since any number raised to the power of 0 is 1. Using the point (0, 16), we substitute x = 0 and y = 16 into the equation y = ab^x to get: 16 = ab^0 Since anything raised to the power of 0 is 1, we have: 16 = a * 1 Therefore, a = 16.Find 'b' value: Now that we have the value of 'a', we can use the second point (2, 784) to find the value of 'b'. We substitute x = 2, y = 784, and a = 16 into the equation y = ab^x to get: 784 = 16b^2 To solve for 'b', we divide both sides by 16: 784 / 16 = b^2 49 = b^2 Taking the square root of both sides gives us two possible solutions, b = 7 or b = -7. Since we are dealing with an exponential function, which typically involves growth or decay, we consider only the positive value for 'b'. Therefore, b = 7.Write exponential function: We have found the values of 'a' and 'b': a = 16 and b = 7. We can now write the equation of the exponential function: y = 16 * 7^x This is the exponential function that passes through the points (0, 16) and (2, 784).

Write an exponential function in the form $y=a b^{x}$ that goes through the points $(0,16)$ and $(2,784)$ . $\newline$ Answer:

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Write an exponential function in the form $y=a b^{x}$ that goes through the points $(0,16)$ and $(2,784)$ . $\newline$ Answer: