Answer:
• A(1)=4
,
• A(2)=8
,
• A(3)=13
,
• A(4)=17.5
Explanation:
The graph is given below:
The area, A(x) represents the area bounded by the graph, the horizontal axis, and the vertical lines at t=0 and t = x.
(a)A(1)
Area, A(1) is the area of a trapezoid in which: a=3, b=5 and h=1
[tex]\begin{gathered} \text{ Area of a trapezoid}=\frac{1}{2}(a+b)h \\ A(1)=\frac{1}{2}(3+5)(1)=\frac{1}{2}\times8=4\text{ square units} \end{gathered}[/tex]
(b)A(2)
.
[tex]A(2)=2\times A(1)=2\times4=8\text{ square units}[/tex]
(c)A(3)
.
[tex]\begin{gathered} A(3)=A(2)+(5\times1) \\ =8+5 \\ =13\text{ square units} \end{gathered}[/tex]
(d)A(4)
[tex]\begin{gathered} A(4)=A(3)+\text{ Area of shape 4} \\ =13+\frac{1}{2}(5+4)(1) \\ =13+\frac{9}{2} \\ =13+4.5 \\ =17.5\text{ square units} \end{gathered}[/tex]
