8. (8 points) Let $$ p(t) $$ denote the position of a particle in cm after $$ t $$ seconds. Suppose that we are unable to write down a nice formula for $$ p(t) $$, but we happen to know that when $$ t=5 $$ seconds, the particle has position 3 cm and velocity $$ -2 \mathrm{~cm} / \mathrm{s} $$. Find the linearization of $$ p(t) $$ at $$ t=5 $$ seconds, and use it to approximate the location of the particle when $$ t=5.2 $$ seconds. (Include units with your answer.)

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The linearization of $$ p(t) $$ at $$ t = 5 $$ seconds is $$ L(t) = 13 - 2t $$. Using this, the particle's approximate location at $$ t = 5.2 $$ seconds is $$ 2.6 $$ cm.

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