Are these verbs can used interchangeably in the sense of "to guess based on some information".
The remains are conjectured to be thousands of years old.
He conjectured that the company would soon be in financial
difficulties.We'll never know exactly how she died; we can only conjecture.
The figures were obtained by extrapolating from past trends.
You can't really extrapolate a trend from such a small sample
These are example sentences I got from the Oxford and Cambridge online dictionaries.They are original sentences.I wrote down many examples to make it easy to compare for ones who would like to answer this question.You can give your own examples as well if you want.
Best Answer
"Extrapolate" is a mathematical term meaning to extend a graph based on known data points. To take a simple case, if you had a graph with the points (1,2), (2,4), and (3,6), these would form a straight line, so you could "extrapolate" by extending that straight line indefinitely. In more complex cases you might say that the points form a parabola or a logarithm curve or whatever, and extend appropriately.
More generally, then, "extrapolate" is used to mean to predict the future based on current trends. This could be in the strict mathematical sense. Like someone might say, "The number of cell phones in the world is increasing at such-and-such a rate, so if we extrapolate from this, within ten years there will be more cell phones in the world than people." It is also used for more general predictions where you couldn't really measure or count. Like, "At the rate that this country is sinking into moral decay, within 20 years we'll be debating whether people have a Constitutional right to rape a 6 year old."
"Conjecture" is a far more general term meaning to speculate or estimate. The connotation of "conjecture" is that it is an informed guess. That is, it's not wild speculation, but it is also not based on any solid evidence. Like if I said, "I think the stock market will go up 20 points next week", you'd probably say that is a wild guess, because I know very little about the stock market. But if an expert stock market analyst said the same thing, you might call that a conjecture.
Proposed mathematical theorems are sometimes called "conjectures". That is, if a mathematician says that intuitively to him, he thinks that some statement about numbers or geometry or whatever is probably true, but he hasn't been able to devise a proof, that is called a conjecture.