The village clinic recorded two cases of an infection on Monday and four on Tuesday. The nurse wrote both numbers on the board and asked the visiting doctor what she expected on Wednesday.
The doctor said that was exactly the right question, and that two numbers were not enough to answer it.
If the infection is adding two cases a day, Wednesday brings six, and by the tenth day the total for that day is twenty. If it is doubling instead, Wednesday brings eight, and by the tenth day it is more than a thousand.
Both patterns produce two and four. They are indistinguishable on the first two days, and they part company on the third. That is why the doctor wanted Wednesday's number before she would say anything, and why she wanted Thursday's before she would trust it.
She also warned the nurse against the opposite error. Three days of doubling does not mean the doubling continues: infections run out of people to reach, just as the model runs out of support beyond the data.
The difference matters because the two answers call for different preparations. Twenty cases in a day is a busy clinic. A thousand is not a clinic problem at all; it is a district one, and the request for help has to be sent while the numbers are still small.
Wednesday brought seven. That is one above the adding model and one below the doubling one, and it settles nothing by itself. The doctor sent the message anyway, and said why: if she is wrong about doubling she has troubled the district office for nothing, and if she is right and waits, she has lost the only week in which the request was easy to answer.