ECONOMICS (CBSE/UGC NET)

Detailed explanation-1: -The function P = P 0 e r t can be used to model population growth where is the initial population, is the growth rate, and is time. The exponential decay function can be written as f ( x ) = a ( 1 − r ) x where is the starting amount and is the rate of decay.

Detailed explanation-2: -The decay rate is expressed as a percentage. We convert it to a decimal by simply reducing the percent and dividing it by 100. Then calculate the decay factor b = 1-r. For instance, if the rate of decay is 25%, the exponential function’s decay rate is 0.25 and the decay factor b = 1-0.25 = 0.75.

Detailed explanation-3: -It can be expressed by the formula y=a(1-b)x wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.

Detailed explanation-4: -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.