Question

The number of bacteria colonies \(h\) hours after the beginning of an experiment is given by the function \(C(h)=3^h-2 h+20\). What does the number 20 represent in the function? A) The final rate of growth, in colonies per hour B) The initial rate of growth, in colonies per hour C) One less than the initial number of bacteria colonies D) One more than the final number of bacteria colonies $$ \begin{aligned} &\text { Agricultural Land as a Percent of Total Land Area, } 2014\\\ &\begin{array}{|l|c|} \hline \multicolumn{1}{|c|}{\text { Country }} & \text { Percent of Total Land Area } \\ \hline \text { Brazil } & 33.8 \% \\ \hline \text { Canada } & 7.2 \% \\ \hline \text { Greenland } & 0.6 \% \\ \hline \text { Latvia } & 30.1 \% \\ \hline \text { Mexico } & 54.9 \% \\ \hline \text { New Zealand } & 42.2 \% \\ \hline \text { Russian Federation } & 13.3 \% \\ \hline \text { Turkey } & 50.1 \% \\ \hline \text { United States } & 44.6 \% \\ \hline \end{array} \end{aligned} $$

Short answer

The number 20 in the function represents one less than the initial number of bacteria colonies. The correct answer is C) One less than the initial number of bacteria colonies.

Step-by-step solution

Write down the given function

The number of bacteria colonies h hours after the beginning of an experiment is given by the function: \[C(h) = 3^h - 2h + 20\]

Calculate the initial number of bacteria colonies

To find the initial number of bacteria colonies (when h = 0), we need to substitute h = 0 into the function: \[C(0) = 3^0 - 2(0) + 20\] \[C(0) = 1 - 0 + 20\] \[C(0) = 21\] This tells us that at the beginning of the experiment, there are 21 bacteria colonies.

Evaluate the answer choices

Now, let's evaluate the different answer choices: A) The final rate of growth, in colonies per hour: this option is not related to the initial conditions of the function, so it is not the correct answer. B) The initial rate of growth, in colonies per hour: this option refers to the initial growth rate, but it is not the number 20 in the function. The initial rate of growth is given by the derivative of the function C(h) evaluated at h=0, which is not 20. Hence, this option is incorrect. C) One less than the initial number of bacteria colonies: Since the initial number of colonies is 21, one less than this number is 20. Therefore, this option is correct. D) One more than the final number of bacteria colonies: This option is not related to the initial conditions of the function, and as such, it is not the correct answer. Based on our evaluation, the correct answer is C) One less than the initial number of bacteria colonies.