# Math

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1. Exponential growth follows the formula y=a(1+r)^x and exponential decay follows the formula y=a(1-r)^x..
This seems obviously TRUE

But now I'm having doubts about the decay formula

Is this true or false?

• Math -

Normally exponential growth is expressed as

f(t) = a e^kt

and exponential decay is

f(t) = a e^-kt

If 0<r<1, then the statement is true, since then we have

1-r < 1 so we have a fraction, and exponential of a fraction is e^-kt for some k.

With no restrictions on r, things get a bit dicier.

I think in your case, say you have a 12% growth rate. Then

f(x) = a(1.12)^x

At 12% decay rate would then mean that 88% is left after each interval, so you would indeed have

f(x) = a(1-.12)^x = a(.88)^x

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