Question

8.3.3 quiz: nonlinear models
what is the exponential regression equation that fits these data?
a. $y = 2.01cdot3.80^{x}$
b. $y = 3.02cdot2.26^{x}$
c. $y = 2.26cdot3.02^{x}$

Explanation:

Step1: Recall the exponential regression formula

The general form of an exponential regression equation is \(y = ab^{x}\), where \(a\) is the initial value (\(y\)-intercept when \(x = 0\)) and \(b\) is the base of the exponential function.

Step2: Check the \(y\)-intercept

When \(x = 0\), from the data table \(y=3\).
For option A: When \(x = 0\), \(y=2.01\times3.80^{0}=2.01\times1 = 2.01
eq3\)
For option B: When \(x = 0\), \(y = 3.02\times2.26^{0}=3.02\times1=3.02\approx3\)
For option C: When \(x = 0\), \(y=2.26\times3.02^{0}=2.26\times1 = 2.26
eq3\)

Answer:

B. \(y = 3.02\cdot2.26^{x}\)