Consider the model

\[
y=\theta_{1}-\theta_{2} e^{-\theta_{3} x}+\varepsilon
\]

This is called the Mitcherlich equation, and it is often used in chemical engineering. For example, \(y\) may be yield and \(x\) may be reaction time.
a. Is this a nonlinear regression model?
b. Discuss how you would obtain reasonable starting values of the parameters \(\theta_{1}, \theta_{2}\), and \(\theta_{3}\).
c. Graph the expectation function for the parameter values \(\theta_{1}=0.5\), \(\theta_{2}=-0.10\), and \(\theta_{3}=0.10\). Discuss the shape of the function.
d. Graph the expectation function for the parameter values \(\theta_{1}=0.5, \theta_{2}=0.10\), and \(\theta_{3}=0.10\). Compare the shape with the one obtained in part \(\mathrm{c}\).