If the allocation doubles every week, that represents exponential growth.
Given there are many types of growth models, and models that grow at a constant rate are linear and models that grow exponentially at an increasing rate.
Linear growth is characterized by growth by the same amount per unit time.
Exponential growth is a process of increasing numbers over time. This happens when the instantaneous rate of change of a quantity over time is proportional to the quantity itself.
Exponential growth because the first week you may only get a dollar, but the next week you get 2, then 4, and so on. Your allowance doesn't grow by the same amount every week, so the number it doubles is exponential.
Therefore, if the allowance doubles every week, it represents a exponential growth multiplier because samples growing at a constant rate are linear.
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