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Water is draining out of a tank so that the height of the water, h m , in time t minutes, satisfies the differential equation dh k h dt = − , where k is a positive constant. The initial height of the water is 2.25 m and 20 minutes later it drops to 1 m. a) Show that the solution of the differential equation can be written as ( )2 60 1600 t h − = . b) Find after how long the height of the water drops to 0.25 m.  In

Water is draining out of a tank so that the height of the water, h m , in time t minutes, satisfies the differential equation dh k h dt = − , where k is a positive constant. The initial height of the water is 2.25 m and 20 minutes later it drops to 1 m. a) Show that the solution of the differential equation can be written as ( )2 60 1600 t h − = . b) Find after how long the height of the water drops to 0.25 m.  In

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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Water is draining out of a tank so that the height of the water, h m , in time t minutes,
satisfies the differential equation
dh k h
dt
= − ,
where k is a positive constant.
The initial height of the water is 2.25 m and 20 minutes later it drops to 1 m.
a) Show that the solution of the differential equation can be written as
( )2
60
1600
t
h
−
= .
b) Find after how long the height of the water drops to 0.25 m. 

In the attached image the prof. solves the equation. Please note the part in the rectangle. What is he doing here. Seems very slick!

 

de =kp? (a) dt o whn teo P: bo0 I=B dP= k dt (000 At + P lo00 p*dP = Jkdt tet P= Z000 -p°= kt + C : 44 + 200 kt t C 4A = - a Att B | %3D 8000 lo00 8 -t 8000 P = BooD 8-t 6) If t-8 P becomts mfinit- P becomts negutivt -la ta a 4.
Transcribed Image Text:de =kp? (a) dt o whn teo P: bo0 I=B dP= k dt (000 At + P lo00 p*dP = Jkdt tet P= Z000 -p°= kt + C : 44 + 200 kt t C 4A = - a Att B | %3D 8000 lo00 8 -t 8000 P = BooD 8-t 6) If t-8 P becomts mfinit- P becomts negutivt -la ta a 4.
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