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 5% per hour.

Question

The initial number of bacteria in the culture is 21.Find the projected population after 24 hours for the following conditions.

 a) No antibiotic is present, so the relative growth rate is 16%.

b) An antibiotic is present in the culture, so the relative growth rate is reduced to 5%.

it says to use the population growth model.

Thanks for the help!

Answer 1

Hi Danny L.,

The formula for growth is A(t) = A_oe^kt, where A(t) is the amount at time t, A_o is the initial amount, and k is a positive constant, and e^(x) is the natural exponential function.

a) With A_o = 21, and k = 0.16 (16%):

A(t) = A_oe^kt,

A(t) = 21e^0.16t,

A(24) = 21e^0.16(24),

A(24) = 977 bacteria

See if you can do b) with k = 0.05 and A_o = 21.

I hope this helps, Joe.