Answer:
D(t) = -t³ + 16t² - 10t + 160
a) D(0) = 160
b) t³ - 16t² + 10t - 160 = 0
t²(t - 16) + 10(t - 16) = 0
(t² + 10)(t - 16) = 0
t = 16 years after 2003
The lake will dry up in 2019.
c) D'(t) = -3t² + 32t - 10
3t² - 32t + 10 = 0
t = (32 ± √((-32)² - 4(3)(10)))/(2(3))
= (32 ± √(1,024 - 120))/6
= (32 + √904)/6
= (32 + 2√226)/6
= (16 + √226)/3
= about 10.34 years after 2003
(sometime in 2013)
D(10.34) = about 661.74 feet
