What conditions will cause a population to have exponential growth?

Exponential growth takes place in Bacteria under ideal conditions. It means a rapid increase in population but actually it is doubling of population in a short time.Under ideal condition generation time of bacteria is just 20 minutes i.e. just after 20 minutes no. of Bacteria is doubled. Initially term used for rapid bacterial growth was logarithmic growthbut that proved to be wrong. Term Exponential growth may also be used for population of higher animals but doubling time is much larger as compared to bacteria.