Growth models (GM) of the mixed-effects and latent curve varieties have become popular methodological tools in lifespan research. One of the major advantages of GM is their flexibility in studying individual differences in change. We scrutinized the change functions of GM used in five years of publications on cognitive aging. Of the 162 publications that we identified, 88% test linear or quadratic polynomials, and fewer than 5% apply functions that are nonlinear in their parameters, such as exponential decline. This apparent bias in favor of polynomial decomposition calls for exploring what conclusions about individual differences in change are likely to be drawn if one applies linear or quadratic GMs to data simulated under a conceptually and empirically plausible model of exponential cognitive decline from adulthood to old age. Hence, we set up a simulation that manipulated the rate of exponential decline, measurement reliability, number of occasions, interval width, and sample size. True rate of decline and interval width influenced results strongly, number of occasions and measurement reliability exerted a moderate effect, and the effects of sample size appeared relatively minor. Critically, our results show that fit statistics generally do not differentiate misspecified linear or quadratic models from the true exponential model. Moreover, power to detect variance in change for the linear and quadratic GMs is low, and estimates of individual differences in level and change can be highly biased by model misspecification. We encourage researchers to also consider plausible nonlinear change functions when studying behavioral development across the lifespan.