Exponential Modelling
Exponential Modelling
- We use \(e^x\) to model situations such as population growth, where the rate of increase is proportional to the size of the data set at any given moment in time.
- Similarly, we can use \(e^{-x}\) to model exponential decay such as radioactive half lives.
Example: \(P=160e^{0.006t}\) where \(t\) is the time in days since the pesticide was first applied
- Estimate \(P\) after 15 days: \(160e^{0.09} = 175.068\)
- Show that \(\frac{dP}{dt}=kP\) where \(k\) is a constant and state the value of \(P\): \(160\times -0.006e^{-0.006t}=-0.96e^{-0.006t}\)
Exercise 14B Q1