For some applications for example when calculating the exponential decay of a radioactive substance an alternative way of writing down the formula for exponential growth and decay is more productive. And so to solve for k we could just say k is equal to the natural log of 12 over minus 5730 which we did in the previous video. If k 0 the function represents exponential decay mathbfa is the initial value.
Where A0 A 0 is equal to the value at time zero e is Eulers constant and k is a positive constant that determines the rate percentage of growth.
So for now well just state that the basic equation for exponential decay is. So now that we have computed the decay factor we get that the exponential decay formula is. Y t a e kt. So for now well just state that the basic equation for exponential decay is.