# To find the volume of water using the function V ( t ) = 50 ( 1 − t 20 ) 2 , 0 &lt; t &lt; 20 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.1, Problem 71E

a.

To determine

## To find the volume of water using the function V(t)=50(1−t20)2,          0<t<20

Expert Solution

The volume of the water for t=0 is V(0)=50 gallons and V(20)=0 gallons for t=20 .

### Explanation of Solution

Given: The function V(t)=50(1t20)2,          0<t<20

Calculation:

Plug t=0 and t=20 in V(t)=50(1t20)2 , then

V(0)=50(1020)2V(0)=50(10)2       =50 gallonsV(20)=50(12020)2V(20)=50(11)2V(20)=50(0)2         =0 gallons

Thus, the volume of the water for t=0 is V(0)=50 gallons and V(20)=0 gallons for t=20 .

b.

To determine

### Representation of the answers obtained in part a.

Expert Solution

The tank initially (t=0 minutes) has a volume of 50 gallons of water while the tank finally (t=20  minutes) has a volume of 0 gallons of water (no water in it).

### Explanation of Solution

It means that the tank initially (t=0 minutes) has a volume of 50 gallons of water while the tank finally (t=20  minutes) has a volume of 0 gallons of water (no water in it).

c.

To determine

### To find the values of the given function of volume of water is V(t)=50(1−t20)2 .

Expert Solution

The values of the function V(t) are shown below:

tV(t)050(1020)2=50550(1520)2=28.1251050(11020)2=12.51550(11520)2=3.1252050(12020)2=0

### Explanation of Solution

Given: The function of volume of water is

V(t)=50(1t20)2

Calculation:

Plug t=0,5,10,15,20 in V(t)=50(1t20)2

V(0)=50(1020)2V(0)=50(10)2       =50 gallonsV(5)=50(1520)2V(5)=50(10.25)2       =50(0.75)2        = 50(.5625)         = 28.125  gallonsV(10)=50(11020)2V(10)=50(10.5)2       =50 (0.5)2        =  12.5  gallonsV(15)=50(11520)2V(15)=50(10.75)2       =50 (0.25)2        =  50 (0.0625)        =   3.125  gallonsV(20)=50(12020)2V(20)=50(11)2V(20)=50(0)2         =0 gallons

Then, the values of the function V(t) are shown below:

tV(t)050(1020)2=50550(1520)2=28.1251050(11020)2=12.51550(11520)2=3.1252050(12020)2=0

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