"Exponential Growth"

 

I recently heard someone say in a television interview that incidence of the corona virus was increasing, but not increasing exponentially. That is an absurd claim.

"exponential" is being misused to mean 'fast' by people who do not know what it means, but use it because they hear clever people using it and think that if they use it they too will appear clever.

A quantity q changes exponentially  when:

q_t =q₀*k^t where q₀ is the initial value of q,

q_t is the value of after t time units, and k is a constant. Positive k corresponds to exponential increase, and negative k to exponential decrease.

Increases of the incidence of the corona virus will always be approximately exponential until near the very end of the epidemic when most people will be immune. Until then the rate at which people catch the virus will be roughly proportional to the number already infectious. That implies exponential growth or decay