Answer
a)1.01
b)1.003
Work Step by Step
To evaluate the function $(1+x)^k$ at x near zero, the given function must be approximated as $1+kx$:
a) $(1.0002)^{50}=(1+.0002)^{50}\approx1+50\times.0002=1.01$
b) $(1.009)^{\frac{1}{3}}=(1+.009)^{\frac{1}{3}}\approx1+\frac{1}{3}\times.009=1.003$
