Previous studies have suggested that children as young as 9 years old have developed an understanding of non-linear growth processes prior to formal education. The present experiment aimed at investigating this competency in even younger samples (i.e., in kindergartners, first, and third graders, ages 6, 7 and 9, respectively). Children (N=90) solved non-verbal inductive reasoning tasks by forecasting linear and exponential growth. While children of all ages forecasted linear growth adequately, exponential growth was also estimated remarkably well. Surprisingly, kindergartners and third graders showed similar high achievement concerning the magnitude and curve shape of forecasts, whereas first graders performed significantly worse. We concluded that primary knowledge of both linearity and non-linearity exists even in kindergartners. However, children's understanding is quite fragile, as their performance was strongly affected by task sequence: Children underestimated exponential growth when the previous task required a forecast of linear growth, and overestimated linear growth when the previous task required forecasting of exponential growth. (Contains 2 tables and 2 figures.)