Question

Someone please explain to me exponential growth and exponential decay? when to use it?

Answer 1

Occurs when something increases or decreases as a fraction of itself, like ten percent per year:

dN/dt = 0.1 N

dN/N = 0.1 dt

integrate

log N = 0.1 t + constant

constant = No, the value when t=0

log(N/No) = 0.1 t

(N/No) = exp(0.1 t)

for 0.1/year and t = 10 years

N/No = 2.72

Instead of doubling in ten years at 10% per year, it increased 2.72x

Exponential decay starts same way, but with dN/dt =- k N

N/No = exp(-kt) is the result

Answer 2

examples: population growth, compound interest
radioactive decay