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

We know that the function passes through the points (0,10) and (2,490).

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

From the point (0,10), we substitute x = 0 and y = 10 into the equation to get:

10 = ab^0
Since any number to the power of 0 is 1, we get a = 10.

Now we know that a = 10, we can use the second point (2,490) to find b. Substituting x = 2, y = 490 and a = 10 into the equation, we get:

490 = 10b^2
Divide both sides by 10 to isolate b^2:

49 = b^2
Taking the square root of both sides, we find that b = 7.

So, the exponential function that passes through the points (0,10) and (2,490) is y = 10*7^x.

Question

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

We know that the function passes through the points (0,10) and (2,490).

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

From the point (0,10), we substitute x = 0 and y = 10 into the equation to get:

10 = ab^0
Since any number to the power of 0 is 1, we get a = 10.

Now we know that a = 10, we can use the second point (2,490) to find b. Substituting x = 2, y = 490 and a = 10 into the equation, we get:

490 = 10b^2
Divide both sides by 10 to isolate b^2:

49 = b^2
Taking the square root of both sides, we find that b = 7.

So, the exponential function that passes through the points (0,10) and (2,490) is y = 10*7^x.

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