Answer:
A. the vertical intercept (often called the y-intercept)
B. the slope of the line
C. V(t) = 100t +2000
D. V(10) = 3000, the value in year 10
E. see attached
Step-by-step explanation:
<h3>a. </h3>You are told that year 0 is the year that you made the investment. Then the value in year 0 represents <em>the value of the investment in the year you made the investment</em>. (It is sometimes called the "initial value.")
When the function is graphed, the value in year 0 will be the value on the graph at t=0. If t=0 is the vertical axis (as it usually is), then 2000 is the vertical intercept--the point where the line meets the vertical axis.
__
<h3>b.</h3>To find the difference between values in consecutive years, subtract one from the other:
2100 -2000 = 100 . . . . the change in value in consecutive years
On the graph, for each increment of 1 in the value of t, the value of the investment will increase by this amount. That means the slope of the graph (rise/run) is 100/1 = 100. The difference in value in consecutive years is the slope of the graph.
__
<h3>c.</h3>The equation of the line is ...
V(t) = (slope) × t + (vertical intercept)
V(t) = 100t +2000
__
<h3>d.</h3>V(10) = 100×10 +2000 = 1000 +2000
V(10) = 3000 . . . . . the value of the investment in year 10
__
<h3>e.</h3>see attached
