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Exponential Growth Law

Let P be the initial amount deposited in an account, and let A be the amount in the account at any time t. In Continuous Compound Interest we notice that rate of growth of A is proportional to A.
Mathematically,
      
Applying initial condition, when t = 0 and A = P
      
By putting e^c = P in the above equation, we have
      
This is same, as the Continuous Compound Interest Formula.

In general, if the rate of change of a quantity Q is proportional to the amount present Q(0) = Q₀ at any time t, we obtain the Exponential Growth Law, as:

Then,

This is called the Exponential Growth Formula.
Where,
Q₀ = Quantity at t = 0 (Initial Quantity)
r = Continuous compound growth rate
t = Time
Q = Quantity at time t

NOTE: If r < 0, then dQ/dt < 0 and Q is decreasing. This type of growth is called Exponential Decay.

Example 1. The number of internet connections in Pakistan are estimated as 4 million in 2013, and the growth rate is 1.5% per year. Find the number of internet connections in Pakistan in 2020.
Solution:
Here, Q₀ = 4 million (initial quantity), r = 1.5% (0.015) and t = 7 (2020-2013=7)
As we know that the formula for exponential growth is:
      
Hence,
      

>> Simple Interest Problems

RELATED PAGES
- Simple Interest
- Simple Interest Problems