$10$:$21$

$65$

$($b$)$ A population changes according to the graph $P^{\text{'}}(t)($hundreds$/$year$)$ below.

$($i$)$ Sketch the rectangles for the Riemann sum $L_3($left with $3$ rectangles$)$ that would be used to estimate ${\displaystyle \underset{0}{\overset{3}{}}}{P}^{\text{'}}(t)dt.$

$($ii$)$ Given that $P(0)=20,$ use the Fundamental Theorem of Calculus and the graph to compute $P(1).$