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

We know that the function passes through the points (0,12) and (4,7500).

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

From the point (0,12), we substitute x = 0 and y = 12 into the equation, we get:

12 = ab^0
Since any number (except 0) to the power of 0 is 1, we have a = 12.

Now, we substitute a = 12 into the equation and use the point (4,7500) to solve for b.

So, 7500 = 12*b^4
Divide both sides by 12, we get b^4 = 625
Take the fourth root of both sides, we get b = 5.

So, the exponential function that goes through the points (0,12) and (4,7500) is y = 12*5^x.

Question

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

We know that the function passes through the points (0,12) and (4,7500).

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

From the point (0,12), we substitute x = 0 and y = 12 into the equation, we get:

12 = ab^0
Since any number (except 0) to the power of 0 is 1, we have a = 12.

Now, we substitute a = 12 into the equation and use the point (4,7500) to solve for b.

So, 7500 = 12*b^4
Divide both sides by 12, we get b^4 = 625
Take the fourth root of both sides, we get b = 5.

So, the exponential function that goes through the points (0,12) and (4,7500) is y = 12*5^x.

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