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.?	Choose the correct choice from the following
A) 13000
B) 12500
C) 13500
D) 14000
E) 15000

Rationale: let the rate be x , then population of the bacteria after each hour can be given as 500,500 x , 500 ( x ^ 2 ) , 500 ( x ^ 3 ) now population at 4 pm = 62,500 thus we have 500 ( x ^ 3 ) = 62,500 = 125 thus x = 5 therefore population at 3 pm = 500 ( 25 ) = 12500 answer : b
Answer: B