A bacterial culture is growing exponentially, and its mass increases from 2 mg to 5 mg in 30 hours. Find the mass of the culture after 25 hours.
We have the following equation
M = ae^(kt)
Where M is the mass after t hours
a = the beginning mass
k is the growth constant
We need to find k thusly
5 = 2e^(k 30) divide both sides by 2
2.5 = e^(30k) take the Ln on both sides
Ln 2.5 = Ln e^(30k) and we can write
Ln 2.5 = 30k * Ln e [Ln e = 1....so we can ignore this ]
Ln 2.5 = 30 k divide both sides by 30
Ln (2.5) /30 = k
After 25 hours we have that
M = 2e^(Ln (2.5)/30* 25) ≈ 4.29 mg