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. Note: Once you find the equation, round a and b to the nearest hundredth to determine the solution. 62,821 78,324 20,864 20,167

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)^t
12.500= 1,000(1+r)^12
1,000(12.5)= 1,000(1+r)^12
12.5= (1+r)^12
1+r= 1.23427
r= 0.23

Number of bacteria after 20hr would be:
an= ao(1+r)^t
an= 1,000(1+0.23)^20
an= 1,000(62.821 )
an= 62,821