Analyzing the misperception of exponential growth in graphs

Exponential growth is frequently underestimated, an error that can have a heavy social cost in the context of epidemics. To clarify its origins, we measured the human capacity (N = 521) to extrapolate linear and exponential trends in scatterplots. Four factors were manipulated: the function underlying the data (linear or exponential), the response modality (pointing or venturing a number), the scale on the y axis (linear or logarithmic), and the amount of noise in the data. While linear extrapolation was precise and largely unbiased, we observed a consistent underestimation of noisy exponential growth, present for both pointing and numerical responses. A biased ideal-observer model could explain these data as an occasional misperception of noisy exponential graphs as quadratic curves. Importantly, this underestimation bias was mitigated by participants' math knowledge, by using a logarithmic scale, and by presenting a noiseless exponential curve rather than a noisy data plot, thus suggesting concrete avenues for interventions.