Wes 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 2,000 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 250,000. 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.?
50,000
62,500
65,000
86,666
125,000
I am going through the above problem from a Manhattan CAT exam. Note the explanation says the following:If we decide to find a constant multiple by the hour, then we can say that the population was multiplied by a certain number three times from 1 p.m. to 4 p.m.: once from 1 to 2 p.m., again from 2 to 3 p.m., and finally from 3 to 4 p.m.
Let's call the constant multiple x.
2,000(x)(x)(x) = 250,000
2,000(x^3) = 250,000
x^3 = 250,000/2,000 = 125
x = 5
Therefore, the population gets five times bigger each hour.
My question is....The problem never states the frequency of increase. How can we say it increased every hr?
50,000
62,500
65,000
86,666
125,000
I am going through the above problem from a Manhattan CAT exam. Note the explanation says the following:If we decide to find a constant multiple by the hour, then we can say that the population was multiplied by a certain number three times from 1 p.m. to 4 p.m.: once from 1 to 2 p.m., again from 2 to 3 p.m., and finally from 3 to 4 p.m.
Let's call the constant multiple x.
2,000(x)(x)(x) = 250,000
2,000(x^3) = 250,000
x^3 = 250,000/2,000 = 125
x = 5
Therefore, the population gets five times bigger each hour.
My question is....The problem never states the frequency of increase. How can we say it increased every hr?
