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What method can be employed to eliminate variable 'a' from the simultaneous equations?
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Division of the two equations
What is the general form of an exponential function used to model data points?
y = a * b^x
How is 'a' calculated after finding 'b', using point (2, 6)?
Substitute b in the equation 6 = a * 2^2, then solve for 'a'.
What mathematical operation helps find the value of 'b' from 1/8 = b^-3?
Raising to the power of -1/3
Calculate 'a' using the equation 6 = a * 2^2.
a = 3/2
Given the point (2, 6), what equation can be formed using the exponential model y = a * b^x?
6 = a * b^2
Why is aligning the equations on top of one another useful?
For easier manipulation and identification of common terms.
What equation corresponds to the point (5, 48) when substituting into y = a * b^x?
48 = a * b^5
How can you simplify the division of the equations 6 = ab^2 and 48 = ab^5?
By dividing, resulting in 1/8 = b^-3
Explain why the function y = (3/2) * 2^x is considered an appropriate model for the points given.
It fits the structure of the exponential function and accurately passes through both given points.
How can you verify the accuracy of the derived exponential function?
By checking if the function passes through the given points using exponential regression or graphing.
After solving for 'b,' what is its calculated value?
b = 2
What is the final exponential function that models the data points (2, 6) and (5, 48)?
y = (3/2) * 2^x
What does the term 'exponential regression' refer to?
A type of regression analysis used to fit an exponential model to data.
In the context of exponential models, what does the base 'b' represent?
The base 'b' represents the rate of growth or decay in the model.
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