The Deepwater Horizon oil spill began on April 20, 2010, and the well was not declared sealed until September of 2010. Suppose that the spill was relatively circular in shape, and that the radius of the spill increased at a rate of approximately $10$ miles per day.

a) Fill in the table below showing the radius in miles, $r$, of the oil spill $t$ days after April 20.

b) Write a formula for $r$ as a function of $t$.
$r(t)=$

c) Venice, Louisiana is approximately 50 miles from the site of the well. Approximately how long did it take for oil to wash up on the shores of Venice? Please round your answer up to the next whole number.
days

d) Assuming the spill was circular, write a formula for the area, $A$, of the oil spill as a function of $t$. Hint: recall that the area of a circle is given by $\pi r^2$.
$A(t)=$

e) How many full days after the initial spill would it take to guarantee the area of the spill was 7000 square miles? Please round your answer up to the next whole number.
days

Hint: