In 1797, a researcher shot a gun with various amounts of gunpowder and measured the forces of the fired gunpowder (see Table 57). Let y be the force (in newtons) of x milligrams of fired gunpowder.

a. Find an equation of the exponential regression equation.
b. Use the model to predict the force of 454 milligrams of fired gunpowder. What is the residual? What does it tell you about the data point and the graph of the model?
c. Use the model to predict the force of 842 milligrams of fired gunpowder. What is the residual? What does it tell you about the data point and the graph of the model?
d. Compute the coefficient of determination for the model. What does it mean in this situation?
e. Construct a residual plot. Even though the coefficient of determination is quite close to 1, explain why the residual plot suggests that there might be a model that fits the data better than the one you found in part (a).

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Table 5Z Amounts of Gunpowder and Forces Gunpowder (milligrams) 65 194 324 454 583 713 842 972 1166 Force (newtons) 255 747 1838 2659 5081 7268 10.754 15.467 35,953