QuestionJuly 15, 2025

Convert your (x,lny) model from the previous slide to an exponential model. A) y=2.2(1.8)^x B) y=5.0(1.5)^x C) y=3.3(1.5)^x D) y=10.0(1.8)^x E) y=8.2(1.5)^x

Convert your (x,lny) model from the previous slide to an exponential model. A) y=2.2(1.8)^x B) y=5.0(1.5)^x C) y=3.3(1.5)^x D) y=10.0(1.8)^x E) y=8.2(1.5)^x
Convert your (x,lny) model from the previous slide to an exponential model. A) y=2.2(1.8)^x B) y=5.0(1.5)^x C) y=3.3(1.5)^x D) y=10.0(1.8)^x E) y=8.2(1.5)^x

Solution
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Answer

A) y=2.2(1.8)^{x} Explanation 1. Identify the form of the model The given model is in the form (x, \ln y). To convert it to an exponential model, recognize that \ln y = a + bx implies y = e^a \cdot e^{bx}. 2. Match with options Compare the exponential form y = e^a \cdot (e^b)^x with the given options. Each option is of the form y = A \cdot B^x, where A = e^a and B = e^b. 3. Determine correct coefficients Without specific values for a and b, we rely on matching the structure. The base B should match the exponential growth factor from the original model's slope b.

Explanation

1. Identify the form of the model<br /> The given model is in the form $(x, \ln y)$. To convert it to an exponential model, recognize that $\ln y = a + bx$ implies $y = e^a \cdot e^{bx}$.<br /><br />2. Match with options<br /> Compare the exponential form $y = e^a \cdot (e^b)^x$ with the given options. Each option is of the form $y = A \cdot B^x$, where $A = e^a$ and $B = e^b$.<br /><br />3. Determine correct coefficients<br /> Without specific values for $a$ and $b$, we rely on matching the structure. The base $B$ should match the exponential growth factor from the original model's slope $b$.
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