Question

Lesson 1-1: The periodic comet named Johnson has been seen at every return since its discovery in 1949, as shown in the table below: Occurrence Year Seen 1- 1949 2 1956 3 1963 4 1970 Use the table for Items 1-5. Describe any pattern you see in the table. Write the values in the second column at the table as a sequence. Identify the common difference. If the pattern continues, in which of the following years will the comet be visible again? A. 2017 B. 2018 C. 2019 D. 2020 About how many times would the Johnson comet be visible during a typical person’s lifetime? Explain your reasoning. 5. Reason abstractly. A man was born during a year in which the Johnson comet was visible in the sky. The next time that the comet was visible after the man’s birth year was in 2005. In what year was the man born? The table to use is attached to the question.

Answer 1

Answer:

Step-by-step explanation:

Occurrence                 Year seen          Difference

1                                      1949                       -  

2                                     1956               1956 - 1949 = 7

3                                     1963               1963 - 1956 = 7

4                                     1970                1970 - 1963 = 7

Difference between each successive term of year seen = 7 years

Therefore, there is a common difference of 7 years between each successive term.

Function defining the year seen will be a linear function and will increase in the same pattern. (multiple of 7 years)

2017 - 1970 = 47 (It's not the multiple of 7)

2018 - 1970 = 48 (It's not the multiple of 7)

2019 - 1970 = 49 (multiple of 7)

2020 - 1970 = 50 (It's not the multiple of 7)

Therefore, comet will be seen next in 2019.

Option (C) will be the answer.

If a person is born in 2005

Then difference between 2005 and 1949 = 56 years

Number of times comet seen after 1949 = $\frac{56}{7}=8$ times

Total number of comet seen in the lifetime = 8 times