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.

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