If some quantity is increasing decreasing by the same proportion or factor in each time interval, then it is said to vary exponentially. A good example is money left in a bank which attracts compound interest at the same rate each year. If the rate of interest is 5%, then at the end of every year the amount of money in the bank is multiplied by 1.05 (). If the amount of money in the bank is initiallythen the amount afteryears isThis equation is of the formwhereandare constants.
We may know that a quantityvaries exponentially, so be able to writewhereandare constants. We want to find the constantsandSuppose thatwhen andwhenSubstituting these values into the expression for Q gives
(2) dividing by (1) gives
Then from (1)
ThenThe graph ofagainstis given below. Notice how the graph curls upwards.