Question

1.Suppose the amount of water collected from a mountain spring decreases over the summer at a rate of 1.5% per day. When will the spring's output fall to four-fifths its present level?
Select one:
a. 61.086 days
b. 34.055 days
c. 14.876 days
d. 3.347 days
e. 52.714 days

2. The point (1,4) lies on the graph of the equation y=f(x) for which dy/dx=3√(xy) where x=>0 and y=>0. When x=0 the value of y is
a. 1
b. 0
c. 3
d. 2
e. 4

Answer 1

#1. solve for t in

0.985^t = 0.8

#2

dy/dx = 3√x √y
dy/√y = 3√x dx
2√y = 2x^(3/2) + c
at (1,4) we have
2√4 = 2*1^(3/2)+c
4 = 2+c
c = 2

2√y = 2x^(3/2)+2
at x=0,
2√y = 2
y = 1

check:
y = (x^(3/2)+1)^2
y' = 2(x^(3/2)+1)(3/2 √x)
= 3√x (x^(3/2)+1)
= 3√(xy)