This exercise uses the population growth model It is observe

This exercise uses the population growth model. It is observed that a certain bacteria culture has a relative growth rate of 16% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 6% per hour. The initial number of bacteria in the culture is 21. Find the projected population after 24 hours for the following conditions. (Round your answers to the nearest whole number.) (a) No antibiotic is present, so the relative growth rate is 16%. bacteria (b) An antibiotic is present in the culture, so the relative growth rate is reduced to 6% Bacteria

Solution

No = 21

N(t) = ?

r1 = 0.16

r2 = 0.06

t = 24 hr

Then

(a) N(t) = No*e^(r*t) = 21*e^(0.16*24) = 977 becteria

(b) N(t) = No*e^(r*t) = 21*e^(0.06*24) = 88.6 becteria