Mike works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 500 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 62,500. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?  Select the correct option.
A) 13000  B) 12500  C) 13500  D) 14000  E) 15000
let the rate be x, then population of the bacteria after each hour can be given as 500,500x, 500(x^2), 500(x^3)   now population at 4pm =62,500   thus we have 500(x^3) = 62,500 =125   thus x=5   therefore population at 3pm = 500(25) = 12500   Answer : 12500
<result>B</result>
Mike works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 500 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 62,500. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?