6. Critique a Fallacy Mrs. Carter asks her class to write the expression for the exponential function with two distinct function values of (-2,1) and (0,49) .Elora says that she needs more information to express the function analytically. What is wrong with Elora's statement? Write the exponential function.

Question

6. Critique a Fallacy Mrs. Carter asks her class to write the expression for the exponential function with two distinct function values of (-2,1) and (0,49) .Elora says that she needs more information to express the function analytically. What is wrong with Elora's statement? Write the exponential function.

Answer 1

To find the exponential function that passes through the points (-2, 1) and (0, 49), we can use the general form of an exponential function: y = ab^x.Using the point (0, 49), we can substitute the values of x and y into the equation to find the value of a:49 = ab^049 = a(1)49 = aNow, using the point (-2, 1), we can substitute the values of x and y into the equation to find the value of b:1 = 49b^-21 = 49/b^2b^2 = 49b = √49b = 7Therefore, the exponential function is y = 49(7)^x.

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