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.

Oofrence Oct 15, 2019

#1**+3 **

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

CPhill Oct 15, 2019