Identify the sequence graphed below and the average rate of change from n = 0 to n = 3.
2 answers:
Answer:
; average rate of change is -35/3.
Step-by-step explanation:
The graph of a sequence has points plotted using the term number as the x-coordinate and the term value as the y-coordinate.
This means the second term of the sequence is 10; the third term is 5; the fourth is 2.5; and the fifth is 1.25.
Looking at the term values, we see that 5 is half of 10; 2.5 is half of 5; and 1.25 is half of 2.5. This means that the common ratio, or constant that the sequence is multiplied by, is 1/2.
We start at the second term; this means the first term we are given, 10, is the second term of the sequence. For this reason, we will use (n-2) as our exponent (using 2 for the second term, we would have an exponent of 0; raising 1/2 to an exponent of 0 gives us the value 1, which will in turn keep our sequence at 10). This gives us
.
Since the term values decrease every time, the rate of change will be negative. Our two options are positive 35/3 or -35/3; the correct choice will be -35/3.
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ANSWERS
(5) Graph:
(6) Solutions: (-1, -5) and (-2, -7)
Not solutions: (1, 1) and (-4, -3)
EXPLANATION
(5) To graph this system, first, we have to graph each of the inequalities. Both are linear, so we have to graph each line with a dashed line - this is because they are "less than" the line, so the line is not included, and shade the area below each of them.
The first inequality is y < -3x-4,
The second inequality is y < 2x - 1,
The graph of the system is the area shared by both graphs,
(6) Any point that is inside the shaded area is a solution of the system. For example, points (-1, -5) and (-2,-7) are solutions to the system.
On the other hand, any point outside that area, or on the dashed lines is not a solution. For example, points (1, 1) and (-4, -3) are not solutions
