Question

1. (5 points) a bacterial culture (in millions) is modeled by the function (b(t)=12 + 4ln(t)), where (t) is measured in hours after the culture is started. find the instantaneous rate of change of the culture size at (t = 4) hours. round your answer to the nearest whole number.

a. 4 million cells per hour
b. 1 million cells per hour
c. 12 million cells per hour
d. 16 million cells per hour
e. none of the above

Explanation:

Step1: Find the derivative of $B(t)$

The derivative of a constant is 0, and the derivative of $\ln(t)$ is $\frac{1}{t}$. Using the sum - rule and constant - multiple rule of differentiation, if $B(t)=12 + 4\ln(t)$, then $B^\prime(t)=0+4\times\frac{1}{t}=\frac{4}{t}$.

Step2: Evaluate the derivative at $t = 4$

Substitute $t = 4$ into $B^\prime(t)$. We get $B^\prime(4)=\frac{4}{4}=1$.

Answer:

B. 1 million cells per hour