The graph shows the depth of water w n a reservoir over a on

The graph shows the depth of water w n a reservoir over a one year period os atuoton of the number of drssnce the begning or year.) yer(Apure )IS dan n W(ft) 100 75 50 25 100 200 300 x(days) (e) Determine the intervais on which the functien W is increasing (Select all that apply (so, 300) (300, 365) Determine the intervals on which the funiction Wis decreasing (Select all that apply.) 10, 150) (150, 300) 1300,365) (b) At what value of x dces w achieve local maximum? days e local minmum tc) Find the rnet change in the depth w from 100 days to 200 days

Solution

1)

a)

W is increasing in (0,150) ,(300,365)

W is decreasing in (150,300)

b)

local maximum at x =150

local minimum at x =300

c)

depth =75 at x=100

depth =50 at x=200

net change in depth =|50-75|

net change in depth =25 ft

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2)

starting year not mentioned in question

a)

P is increasing in (0,20) ,(20,25)

P is decreasing in(25,40),(40,50)

b)

maximum population =50 thousand people

attained 25years from starting year

c)

net change =|population in year 2000 -population in year 1990|

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3)

(1_/(x+2))²-2(1_/(x+2)) -24=0

x+2 0

=>x-2

(1_/(x+2))²-2(1_/(x+2)) -24=0

=>(1-2(x+2) -24(x+2)²)_/(x+2)²=0

=>(1-2(x+2) -24(x+2)²)=0,x-2

=>-24x²-98x-99=0,x-2

=>-(6x+11)(4x+9)=0,x-2

=>x=-11_/6,x=-9_/4