77.

1. Zeros: $x=0,$ multiplicity 2; $x=4,$ multiplicity 1

2. 

3. 2

4. Domain: [0, 4]. The portion between the x-intercepts constitutes the graph of R(x)

79.

1. [0, 1]

2. 

81.

1. $R(x)=27x-{\displaystyle \frac{1}{90,000}}{x}^3$

2. $[0,900\sqrt{3}]$

3. 

83.

1. $N(x)=(x+12)(400-2x^2)$

2. $[0,10\sqrt{2}]$

3. 

85.

1. $V(x)=x(8-2x)(15-2x)$

2. 

87.

1. $V(x)=x^2(108-4x)$

2. 

89.

1. $V(x)=x^2(62-2x)$

2. 

91.

1. $V(x)=2x^2(45-3x)$

2. 

93.

95.

1. $f(7)=1.73\text{ trillions}$

2. two turning points, one zero

3. At $x=3.27\approx 3$ (year 2011), which fits the original data