A positive quantity undergoes exponential growth at constant rate r>0 when y′=ry. For y0>0, the solution of a differential equation is y(t)=y0ert. Every interval of duration Δt multiplies the value by the same factor erΔt, independently of its starting value.
Exponential growth refers to a process where the quantity increases at a rate proportional to its current value. This means that the larger the quantity becomes, the faster it grows.
