Research scientists need a certain type of bacteria to conduct an experiment. There are 2,500 bacteria in a certain culture. The culture grows at a rate of 25% daily. The scientists needs at least 10,000 bacteria to conduct an experiment. What is the least number of days they need to wait for the bacteria culture to reach a quantity of 10,000? (Hint: use a guess-and-check method to determine the lowest number of days that satisfy the requirement.)
A.
5 days
B.
6 days
C.
7 days
D.
10 days

Question

Research scientists need a certain type of bacteria to conduct an experiment. There are 2,500 bacteria in a certain culture. The culture grows at a rate of 25% daily. The scientists needs at least 10,000 bacteria to conduct an experiment. What is the least number of days they need to wait for the bacteria culture to reach a quantity of 10,000? (Hint: use a guess-and-check method to determine the lowest number of days that satisfy the requirement.)
A.
5 days
B.
6 days
C.
7 days
D.
10 days

imstuck · Answer

I got 7 days.  I did it the long way, but here it is:  I started out with 2500 and at the end of day 1 we had the initial 2500 + 25% of 2500 = 2500+625=3125.  Then at the end of the second day I had 3125 + (25%*3125)=3125+781.25=3906.25.  Go on like this and at the end of 7 days you will have 11,920.92