This is the type of growth experienced by a population that increases at a rate proportional to its size. The larger the population gets, the faster it grows

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This sounds like exponential growth. It’s the type of growth you will see in bacterial colonies (for one example) because they grow and multiply so fast.
Answer:  This description refers to "exponential growth" — commonly referenced to as the "J-curve" (from the shape of the graph of "exponential growth" of a population—e.g. human population growth; or bacteria growth);  like the capital letter, "J" . 
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