Chapter 12 - Sequences and Series - 12.3 Taylor Polynomials at 0 - 12.3 Exercises - Page 632: 42

0.96

The profit when x thousand tons of apples are sold is $C(x)=e^{-x/50}$ $C'(x)=\frac{-1}{50}e^{-x/50}$ $C''(x)=\frac{1}{2500}e^{-x/50}$ $C(0)=1$ $C'(0)=\frac{-1}{50}$ $C''(0)=\frac{1}{2500}$ $P_2(x)=1-\frac{1}{50}+\frac{\frac{1}{2500}}{2!}x^{2}$ $P_{2}(x)=\frac{49}{50}-\frac{1}{1250}x^{2}$ $P_{2}(5)=\frac{49}{50}-\frac{1}{1250}(5)^{2} =\frac{24}{25}=0.96$