A certain bacteria infection was detected in a prestigious h

A certain bacteria infection was detected in a prestigious hospital and reported to the administrative staff at 2:00PM on Friday, March 26th,2015. At that time the bacterial count was 80,000 organisms per cm². At 3:30 PM on the same day, the count had risen to 120,000 organisms per cm². 1. Sketch the graph of bacterial growth. 2. Write the equations that predicts the bacterial growth over time. 3. Find the rate at which the infection is increasing. (show calculations) 4. Based upon your mathematics, what time did the infection begon?

Solution

At 2.00pm no. of bacteria = 80,000

At 3.30pm no. of bacteria = 120,000   (1.5 hrs)

N = Noe^(kt) = 80,000e^kt

120,000 = 80000e^(1.5k)

0.405 = 1.5k

k = 0.405/1.5 = 0.27

So, equation: N(t) = 80,000e^(0.27t)

Rate of growth = k = 0.27 = 27%

Infection began at t= 0 i.e. 2.00 pm whe it was reported