Someone please help me

Question

A bacteria culture initially contains 1500 bacteria and doubles every half hour.

1. Find the size of the baterial population after 20 minutes.
2. Find the size of the baterial population after 8 hours.

Answer 1

P=1500

A=Pe^rt

3000=1500e^30r

2=e^30r

ln2=30r

r=ln2/30= growth rate

A=1500e^(20ln2/30) = about 2381.102 after 20 minutes

or, with another method:

A = 1500(2^(2/3))= 1500(1.5874)= about 2381.102 after 20 minutes

A=1500e^(480ln2/30) = 1500e^16ln2

= 98,304,000 after 8 hours=480 minutes

or

A=1500(2^16)=1,500(65,536)= 98,304,000