Answering the following

Question

1. The bacillus bacterium reproduces every 3 hours. If you start with 5 bacterium how long until you have 100,000?

 

2. The magnitude of change is dependent upon the relationship to the buy in such that: M=25(3)2h What value of buy is needed to get a magnitude of 800?  

Answer 1

a_t = a₁(2)^t/h, where a₁ = initial amount, h = half life, t = time elapsed

 

100000 = 5(2)^t/3

20000 = (2)^t/3

ln 20000 = (t/3) ln 2

9.903 ≈ (t/3) ln 2

29.710 ≈ t ln 2

29.710 ≈ 0.931t

31.91 ≈ t