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

We know that the function passes through the points (0,3) and (2,243).

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

From the point (0,3), we substitute x = 0 and y = 3 into the equation:

3 = ab^0
Since any number to the power of 0 is 1, we get a = 3.

Now, we substitute a = 3 into the equation and use the point (2,243):

243 = 3b^2
Divide both sides by 3 to solve for b^2:

81 = b^2
Take the square root of both sides to solve for b:

b = 9

So, the exponential function that passes through the points (0,3) and (2,243) is y = 3*9^x.

Question

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

We know that the function passes through the points (0,3) and (2,243).

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

From the point (0,3), we substitute x = 0 and y = 3 into the equation:

3 = ab^0
Since any number to the power of 0 is 1, we get a = 3.

Now, we substitute a = 3 into the equation and use the point (2,243):

243 = 3b^2
Divide both sides by 3 to solve for b^2:

81 = b^2
Take the square root of both sides to solve for b:

b = 9

So, the exponential function that passes through the points (0,3) and (2,243) is y = 3*9^x.

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