Questions: In the exponential model f(x)=a(1+r)^x, the parameter a is the Select an answer and r is the Select an answer

Transcript text: In the exponential model $f(x)=a(1+r)^{x}$, the parameter $a$ is the Select an answer $\vee$ and $r$ is the Select an answer $\checkmark$

Solution

Solution Steps

Step 1: Identify the parameters in the exponential model

The given exponential model is $ f(x) = a(1 + r)^x $. Here, $ a $ and $ r $ are parameters that define the behavior of the function.

Step 2: Determine the meaning of $ a $

In the exponential model $ f(x) = a(1 + r)^x $, the parameter $ a $ represents the initial amount. This is because when $ x = 0 $, $ f(0) = a(1 + r)^0 = a $, which is the starting value of the function.

Step 3: Determine the meaning of $ r $

In the same model, the parameter $ r $ represents the growth rate. This is because $ (1 + r) $ is the factor by which the function grows or decays over each unit increase in $ x $. If $ r > 0 $, it indicates growth, and if $ r < 0 $, it indicates decay.

Final Answer

The parameter $ a $ is the initial amount and $ r $ is the growth rate. Thus, the final answer is: $\boxed{a \text{ is the initial amount, } r \text{ is the growth rate}}$

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