write an equation of an exponential function that passes through the points (2, 200) and (-1, 102.4)

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Understand Exponential Function: Understand the general form of an exponential function. An exponential function can be written in the form y = ab^x, where a is the initial value, b is the base of the exponential function, and x is the variable.Create Equation with First Point: Use the first point (2, 200) to create an equation. Substitute x = 2 and y = 200 into the general form y = ab^x to get 200 = ab^2.Create Equation with Second Point: Use the second point (-1, 102.4) to create another equation. Substitute x = -1 and y = 102.4 into the general form y = ab^x to get 102.4 = ab^(-1).Solve System of Equations: Solve the system of equations to find the values of a and b. We have two equations: 1) 200 = ab^2 2) 102.4 = ab^(-1) We can solve for a and b using these two equations.Solve for a: Solve for a from the second equation. From the second equation, we can isolate a by multiplying both sides by b to get 102.4b = a.Substitute for a in First Equation: Substitute the expression for a into the first equation. Substitute 102.4b for a in the first equation to get 200 = 102.4b * b^2.Simplify Equation for b: Simplify the equation to solve for b. Simplify the equation to get 200 = 102.4b^3. Now, divide both sides by 102.4 to solve for b^3. b^3 = 200 / 102.4 b^3 = 1.953125Find Value of b: Find the value of b by taking the cube root of both sides. b = (1.953125)^(1/3) b ≈ 1.25Substitute for a: Substitute the value of b back into the equation for a. Now that we have b, we can find a using the equation 102.4b = a. a = 102.4 * 1.25 a = 128Write Final Exponential Function: Write the final equation of the exponential function. Now that we have both a and b, we can write the equation of the exponential function as y = ab^x. y = 128 * 1.25^x

write an equation of an exponential function that passes through the points $(2, 200)$ and $(-1, 102.4)$

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write an equation of an exponential function that passes through the points (2,200)(2, 200)(2,200) and (−1,102.4)(-1, 102.4)(−1,102.4)

write an equation of an exponential function that passes through the points $(2, 200)$ and $(-1, 102.4)$