Question

Exact exponential growth

Answer 1

Doubling time. The doubling time of a population exhibiting exponential growth is the time required for a population to double. ... If , then the population is exhibiting exponential growth; if 0 < b < 1 , then the population is exhibiting exponential decay.

An exponential function with the form f(x)=bx f ( x ) = b x , b>0 , b≠1 b ≠ 1 , has these characteristics: one-to-one function. horizontal asymptote: y=0. domain: (−∞,∞)

Exponential word problems almost always work off the growth / decay formula, A = Pe^rt, where "A" is the ending amount of whatever you're dealing with (money, bacteria growing in a petri dish, radioactive decay of an element highlighting your X-ray), "P" is the beginning amount of that same "whatever", "r" is the growth or decay rate, and "t" is time. The above formula is related to the compound-interest formula, and represents the case of the interest being compounded "continuously".

Note that the variables may change from one problem to another, or from one context to another, but that the structure of the equation is always the same