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

Studdy Solution

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 $x$ .
3. The function is in the form $y = a \cdot b^{(x-c)}$ , where $a$ is the initial amount, $b$ is the base of the exponential function, and $c$ 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:
$y = 104100(1.02)^{(x-1960)}$
The base is the number inside the parentheses, which is $1.02$ .

STEP 4

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

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