Suppose you won Michigan's Mega Millions lottery ticket $($by matching $3$ white balls $+$ mega ball$)$ and invested your $$200$ payout in a savings account chosen by me$.$ Your account balance is provided in the table.

a$.$ Find the growth factor and growth rate

b$.$ Interpret the growth rate$/$factor in the context of the situation.

$\backslash$table$[[$Years$,$Account Balance$],[0,200\mathrm{.}00],[1,210\mathrm{.}00],[2,220\mathrm{.}50],[3,231\mathrm{.}53],[4,243\mathrm{.}10],[5,255\mathrm{.}26],[6,268\mathrm{.}02]]$

c$.$ Write an equation to model the situation.

d$.$ What will your account be worth in $70$ years?

e$.$ When will the account be worth $$20,000?$ Sketch the graph.

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