Question

The population of a colony of 300 bacteria grows exponentially. After 2 hours, the population reaches 500. How much time will it take for the population to reach 9,600

Answer 1

t = 13.56915448 hrs.

Explanation:

500 = 300
`e^(2k)`

5/3 =
`e^(2k)`

ln(5/3) = 2k ln(e)

k = ln(5/3)/2

k= 0.255412812

~~~~~~~~~~~~

9600 = 300
`e^(0.255412812 t)`

32=
`e^(0.255412812 t)`

ln(32) =
`0.255412812 t` ln(e)

t = ln(32)/0.255412812

t = 13.56915448 hrs.