Transcription of P t) = P model. The constant is called b The growth rate ...
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P t) = P model. The constant is called b The growth rate ...
A function which models exponential growth or decay can be written in either the formP(t) =P0btorP(t) = either form,P0represents the initial formP(t) =P0ektis sometimes called thecontinuous exponentialmodel. The constantkis calledthecontinuous growth (or decay) rate. In the formP(t) =P0bt, thegrowth rateisr=b 1. The constantbis sometimes called the growth growth rate and growth factor are not the is a simple matter to change from one model to the other. If we are givenP(t) =P0ekt, and wantto write it in the formP(t) =P0bt, all that is needed is to note thatP(t) =P0ekt=P0(ek)t, so if we letb=ek, we have the desired form. If we want to switch fromP(t) =P0bttoP(t) =P0ekt, it again is just amatter of noting thatb=ek, and solving forkin this case. That is,k= for solving problems:Given a rate of growth or decayr, Ifris given as a constant rate of change (some fixed quantity per unit), then the equation is linear( +rt) Ifris given as a percentage increase or decrease, then the equation is exponential if the rate of growth isr, then use the modelP(t) =P0bt, whereb= 1 +r if the rate of decay isr, then use the modelP(t) =P0bt, whereb= 1 r if thecontinuousrate of growt
0ekt is sometimes called the continuous exponential model. The constant k is called the continuous growth (or decay) rate. In the form P(t) = P 0bt, the growth rate is r = b 1. The constant b is sometimes called the growth factor. The growth rate and growth factor are not the same. It is a simple matter to change from one model to the other.
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