CPM Homework Help : A2C Problem 2-138

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2-138.

Find a rule for each sequence below. Then describe its graph.

$n$
$t\left(n\right)$
$3$
$8$
$5$
$2$
$7$
$−4$
Hint (a):
First, decide if the given sequence is arithmetic or geometric.
Step 1(a):
Common difference =
$\frac{\Delta t(n)}{\Delta n} = \frac{2 -8 }{5 -3} = \frac{-6}{2}=-3$
So, $t\left(n\right) = −3n + b.$
Step 2(a):
Find the value of b at $\left(3, 8\right)$ .
Step 3(a):
Write the equation once you know b. Then describe the graph.
Answer (a):
$t\left(n\right) = −3n + 17$
The graph is a straight line with the y-intercept at (0, 17) and a slope of −3.

$n$
$t\left(n\right)$
$1$
$40$
$2$
$32$
$3$
$25.6$
Hint (b):
The multiplier is less than $1$ .
Hint 2(b):
You will need to find t(0) to write the equation.
More Help (b):
This graph is not linear.

Use the eTool below to view the graphs.
Click the link at right for the full version of the eTool: A2C 2-138 HW eTool

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