ECONOMICS (CBSE/UGC NET)

Detailed explanation-1: -A function which models exponential growth or decay can be written in either the form P(t) = P0bt or P(t) = P0ekt. In either form, P0 represents the initial amount. The form P(t) = P0ekt is sometimes called the continuous exponential model. The constant k is called the continuous growth (or decay) rate.

Detailed explanation-2: -A quantity is subject to exponential decay when it decreases at a rate proportional to its current value. The formula for calculating decay is V f = V i • r t where is the final value, is the initial value, r is the depreciation rate (or decay factor), and f is time.

Detailed explanation-3: -Continuous Exponential Growth/Decay Formula: The formula for continuous exponential growth/decay is given by P=P0ekt P = P 0 e k t where P is the ending amount, P0 is the starting amount, k is the growth/decay rate, and t is time.

Detailed explanation-4: -To find exponential growth or decay models, identify the initial amount and the growth or decay rate. You can use either A ( t ) = A 0 ( 1 + r ) t (growth), A ( t ) = A 0 ( 1 − r ) t (decay), or A ( t ) = A 0 e k t (growth or decay depending on ) for exponential models.