The general form of an exponential function is y = ab^x.

We know that the function passes through the points (0,7) and (2,567).

We can use these points to form two equations and solve for a and b.

From the point (0,7), we substitute x = 0 and y = 7 into the equation to get:

7 = ab^0
Since any number to the power of 0 is 1, we get a = 7.

Now we know that a = 7, we can use the second point (2,567) to find b. Substituting x = 2, y = 567, and a = 7 into the equation, we get:

567 = 7b^2
To solve for b, we first divide both sides by 7 to get:

81 = b^2
Then, we take the square root of both sides to get:

b = 9

So, the exponential function that goes through the points (0,7) and (2,567) is y = 7*9^x.

Question

The general form of an exponential function is y = ab^x.

We know that the function passes through the points (0,7) and (2,567).

We can use these points to form two equations and solve for a and b.

From the point (0,7), we substitute x = 0 and y = 7 into the equation to get:

7 = ab^0
Since any number to the power of 0 is 1, we get a = 7.

Now we know that a = 7, we can use the second point (2,567) to find b. Substituting x = 2, y = 567, and a = 7 into the equation, we get:

567 = 7b^2
To solve for b, we first divide both sides by 7 to get:

81 = b^2
Then, we take the square root of both sides to get:

b = 9

So, the exponential function that goes through the points (0,7) and (2,567) is y = 7*9^x.

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