Question

question
each table displays a linear or an exponential relationship modeling a situation. use the patterns in the tables to find the missing values.
type the correct answer in each box. use numerals instead of words.
situation w
situation z
x | y
11 | 62
12 | 67
13 | 72
14 | 77
15 | 82
x | y
0 | 2
1 | 6
2 | 18
3 | 54
4 | 162

Explanation:

Step1: Analyze Situation W

Check the difference between consecutive y - values. For \(x = 11,y = 62\); \(x = 12,y = 67\); \(x = 13,y = 72\). The difference \(67 - 62=5\), \(72 - 67 = 5\), \(77-72 = 5\), \(82 - 77=5\). So the pattern is linear with a common difference of 5. The missing value at \(x = 12\) is already filled as 67 (since \(62 + 5=67\)).

Step2: Analyze Situation Z

Check the ratio between consecutive y - values. For \(x = 0,y = 2\); \(x = 1,y = 6\), ratio \(\frac{6}{2}=3\); \(x = 2,y = 18\), ratio \(\frac{18}{6}=3\); \(x = 3,y=\text{?}\), \(x = 4,y = 162\). The ratio between \(y\) - values is 3 (exponential growth). So for \(x = 3\), \(y=18\times3 = 54\) (which is already filled), and to confirm, \(54\times3=162\) (matches \(x = 4\) value).

Answer:

For Situation W, the missing value (already filled) is 67. For Situation Z, the missing value (already filled) is 54. (If we assume the question was to verify these, the answers are 67 for Situation W at \(x = 12\) and 54 for Situation Z at \(x = 3\))