How do pocket calculators calculate exponents?

I'd like to know specifically how a pocket calculator (TI calculators also apply) calculates $e^{0.1}$, and what methods or algorithms pocket calculators use in order to produce their answer.

I would be surprised if they actually used Taylor series. For example, the basic 80x87 "exponential" instruction is F2XM1 which computes $2^x-1$ for $0 \le x \le 0.5$. I don't think the implementation is documented, but if I were programming this, I might use a minimax polynomial or rational approximation: the following polynomial of degree $9$ approximates $2^x - 1$ on this interval with maximum error approximately $1.57 \times 10^{-17}$:

-0.15639e-16+(.69314718055995154416+(.24022650695869054994+
(0.55504108675285271942e-1+(0.96181289721472527028e-2
+(0.13333568212100120656e-2+(0.15403075872034576440e-3
+(0.15265399313676342402e-4+(0.13003468358428470167e-5
+0.12113766044841794408e-6*x)*x)*x)*x)*x)*x)*x)*x)*x

By contrast, the Maclaurin polynomial of the same degree has maximum error about $7.11 \times 10^{-12}$ on this interval.

A commonly used set of algorithms is known as CORDIC: COordinate Rotation DIgital Computer. Basically, it uses a bunch of bitshifts, adds, subtracts and look up tables. Its good for cases where you don't have hardware multipliers and what not.

You can also truncate series as well.

An interesting thing is that you can often do some math and identify which chip is used in a calculator. I believe datamath.org has some information on this.