find size after t time

Question

A bacteria culture initially contains 2000 bacteria and doubles every half hour.

 

Find the size of the baterial population after 20 minutes.

Find the size of the baterial population after 6 hours.

Answer 1

doubling time = 1/2 hr

time zero has 2,000 bacteria

in 1 hour 4K, 1.5 hr 8k

2 r 16K, 2.5 hr 32K 3 hr 64K

3.5 hr 128K, 4 hr 256K

4.5 hr 512K 5 hr 1024K 5.5 hr 2048K

6 hours 4,096,000

in 20 minutes= 1/3 hour will less than double <2K

P(t) =2,000(2)^2t

P(6) = 2K(2^12)=4,096,000

P(2/3) = 2K(2^(2/3) = about 3175