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An exponential model for the number of squirrels in a certain area estimates that there were $200$ squirrels in the area in the year $2003$, and that at the end of each $4$-year period for the next $20$ years, the number of squirrels in the area was $120\%$ more than the number at the end of the previous $4$-year period. Which of the following equations represents this model, where $N$ is the estimated number of squirrels in this area $t$ years after $2003$, and $0\le t\le 20$?

A

$N=200(2.20{)}^{4t}$

B

$N=200(1.20{)}^{4t}$

C

$N=200(1.20{)}^{\frac{t}{4}}$

D

$N=200(2.20{)}^{\frac{t}{4}}$