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Math

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PROBLEM

Determine the base function using easy methods for the exponential growth function:
y=104100(1.02)(x1960) y = 104100(1.02)^{(x-1960)}

STEP 1

1. The given function is an exponential growth function.
2. The base of the exponential function is the value inside the parentheses, which is raised to the power of the variable x x .
3. The function is in the form y=ab(xc) y = a \cdot b^{(x-c)} , where a a is the initial amount, b b is the base of the exponential function, and c c is a constant.

STEP 2

1. Identify the base of the exponential function.
2. Confirm the base represents growth.

STEP 3

Identify the base of the exponential function. In the given function:
y=104100(1.02)(x1960) y = 104100(1.02)^{(x-1960)} The base is the number inside the parentheses, which is 1.02 1.02 .

SOLUTION

Confirm that the base represents growth. For exponential growth, the base b b should be greater than 1.
In this case, the base 1.02 1.02 is greater than 1, indicating that it is indeed a growth function.
The base function for the exponential growth is 1.02 \boxed{1.02} .

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