physics radioactivity count rate gcse question

a table is shown and it says
time in seconds: count rate:
0 400
40 283
80 200
120 141
160 100

use the table to calculate the count rate after 200sec?
the answer that the mark scheme has provided is 71 sec( accept 71) but i don't understand why that's the answer.

edit: the table is messed up but the first column if for the time in seconds(e.g. 0,40 etc.) and second column is count rate(e.g. 400, 283 etc.)

(edited 4 years ago)

Reply 1

username4994376

You can work out the half-life by working out how long it takes for the count rate to be halved. In this case, the count rate is halved from 400 to 200 after 80 seconds, i.e the half life is 80 seconds. This means that 80 seconds after 120 seconds (200 seconds), the count rate will be half that of the count rate at 120 seconds. The count rate at 120s is 141, and 141/2 is 70.5 (71) and so your answer is 71.