A culture of bacteria begins with 311 bacteria and every 4 d

A culture of bacteria begins with 311 bacteria, and every 4 days 23 % of the bacteria dies off. Let b b be the 1-day growth factor. a. What is the 4 day growth factor as a numeric value. b. what is the 4 day growth factor in terms of b. Please provide an explanation as to why the answer is true.

Solution

Every 4 days 23% dies off....

As in 77% remains after 4 days

So, equation is of the form :
y = y0 * (0.77)^(t/4)

y = y0 * (0.9367478)^t

Converting this to in terms of k :
e^k = 0.9367478

k = ln(0.9367478)

k = -0.06534 ---> one day growth factor

4 day growth factor :
e^L = 0.77

L = ln(0.77)

L = -0.26136 ---> one day growth factor

Clearly, we can see that L = 4*k

So, one day growth factor is 4 times the 4-day growth factor