Question

8.4.3 test (cst): data and mathematical modeling
what is the exponential regression equation that fits these data?
a. $y = 41.32x^{2}-181.7x + 171.6$
b. $y = 1.22(2.84^{x})$
c. $y = 2.84(1.22^{x})$

Explanation:

Step1: Recall the form of an exponential regression equation

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

Step2: Analyze each option

• Option A: \(y = 41.32x^{2}-181.7x + 171.6\) is a quadratic equation (not exponential as it has a \(x^{2}\) term).
• Option B: \(y=1.22(2.84^{x})\) is in the form \(y = ab^{x}\).
• Option C: \(y = 2.84(1.22^{x})\). When \(x = 1\), \(y=2.84\times1.22=3.464

eq4\). When \(x = 2\), \(y = 2.84\times(1.22)^{2}=2.84\times1.4884 = 4.227
eq8\).
When \(x = 1\) in \(y = 1.22(2.84^{x})\), \(y=1.22\times2.84 = 3.464\approx4\) (approximate due to regression nature). When \(x = 2\), \(y=1.22\times(2.84)^{2}=1.22\times8.0656\approx9.84\approx8\) (again, regression gives approximate values).

Answer:

B. \(y = 1.22(2.84^{x})\)