What a forgetting curve actually is
A forgetting curve is a line drawn through measurements of how much material is retained after different delays. The shape of that line is the model: an exponential curve drops quickly at first and then flattens, while power and hyperbolic curves decline more gradually and stretch out over longer intervals. Choosing among them is not just a mathematical nicety—it changes predictions about how much will be remembered after a day, a week, or a year.
The classic replication target is Ebbinghaus's nineteenth-century work with nonsense syllables. In a modern replication study, retention of nonsense syllables was found to follow an exponential forgetting curve [2]. That is a real fit to real replication data, but it is a single model reported without a side-by-side comparison against power or hyperbolic alternatives, so it cannot by itself establish that the exponential form is the better description.
Do power and hyperbolic curves fit better?
The broadest evidence comes from a review that fitted 210 published datasets to multiple retention functions, including power, hyperbolic, and exponential forms, as well as an exponential function in the square root of time [1]. The takeaway is not that one function wins outright: several of these forms describe forgetting curves reasonably well, and the review treats the exponential-in-square-root-of-time as one of the serious contenders.
That matters for the comparison question. If power, hyperbolic, and exponential variants all produce acceptable fits across many datasets, then the choice among them depends on the range of delays tested and the purpose of the model, not on a single decisive advantage for the exponential form. The review's own framing suggests that replication would not greatly alter a curve fit [1]—in other words, the shape is fairly robust to repeating the measurement, which cuts both ways: it supports the general curve, not one function over its rivals.
What replication data can and cannot settle
Replication data are valuable because they test whether a curve found once reappears under fresh measurement. The nonsense-syllable replication did reproduce an exponential pattern [2], which is consistent with the exponential family being a workable description of retention. But a reproduced fit is not a comparative test. To show that exponential beats power or hyperbolic, a study needs to fit all the candidates to the same replication data and compare them directly, and the replication analysis here does not do that [2].
There is also a scope issue in the larger review: its 210 datasets are published retention data, not replication data specifically [1]. So its conclusion that multiple decay functions fit comparably is strong evidence about forgetting curves in general, but it is one step removed from the narrower question of replication datasets. The two sources together support a modest claim—exponential models fit, and alternatives fit too—rather than a ranking.
So which model should you trust?
If you need a single description of forgetting, an exponential curve is a defensible choice, and it has been observed in replication data for nonsense syllables [2]. If you need to predict retention over very long delays or to compare theories of memory decay, the evidence favors treating power, hyperbolic, and exponential-in-square-root-of-time forms as live alternatives rather than assuming the plain exponential is best [1].
The unresolved piece is direct comparison on replication data. Neither source supplies a head-to-head fit of exponential versus alternative decay functions to the same replication dataset, so the comparative question remains open. What the evidence does support is that forgetting curves are regular enough to be modeled, and that the exponential form is one reasonable member of a family of curves that describe them.
Sources used in this answer
One hundred years of forgetting: A quantitative description of retention.
A review fitting 210 published datasets found that power, hyperbolic, exponential, and exponential-in-square-root-of-time retention functions all describe forgetting curves, with replication not expected to greatly alter a curve fit.
8 Memory I
A replication study of Ebbinghaus-style nonsense-syllable memory reported an exponential forgetting curve, without comparing it to alternative decay functions.