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.

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Miracle Brock

Mathematics

26 July, 07:10

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.

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Baird · 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