Question

what is the difference between the Exponential Growth formula and the Exponential Decay formula?

Answer 1

Let us define Exponential growth

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Where y is the variable increasing , t is independent variable on which y depends

Hence y increases exponentially as a function of t

a is constant , i.e initial value of y at t=0

At t=0 we have y=a

One can understand more clearly if we say by taking log on both sides

Hence this shows log(y) increases linearly with t, hence y increases exponentially with t

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Let us define Exponential decay

         ---------------(1)

Where y is the variable decreasing , t is independent variable on which y depends

Hence y decreases exponentially as a function of t

a is constant , i.e initial value of y at t=0

At t=0 we have y=a

We can again understand more clearly if we say by taking log on both sides

Hence this shows log(y) decreases linearly with t, hence y decreases exponentially with t

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Let us draw plots for both

Here a=1 for exponential growth ,a=7 for exponential decay