Question

A biologist is researching a newly-discovered species of bacteria. He puts 1,000 bacteria into what he has determined to be a favorable growth medium. 12 hours later, he measures 12,500 bacteria. Assuming exponential growth, find the growth equation and use it to determine the number of bacteria after 20 hours.

Answer 1

The bacteria grow from 1,000 bacteria into 12,500 bacteria in 12 hours.  The exponent function would be
:an= ao(1+r)^t12.500= 1,000(1+r)^121,000(12.5)= 1,000(1+r)^1212.5= (1+r)^121+r= 1.23427r= 0.23Number of bacteria after 20hr would be:an= ao(1+r)^tan= 1,000(1+0.23)^20an= 1,000(62.821 )an= 62,821