The number of bacteria colonies h hours after the beginning of an experiment is given by the function `C(h)=3^h-2h+20`. What does the number 20 represent in the function?

Options

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.

Answer

To determine what the number 20 represents in the function \( C(h) = 3^h - 2h + 20 \), we will analyze the function step by step.

### Step 1: Understand the function
The function \( C(h) \) gives the number of bacteria colonies \( h \) hours after the beginning of an experiment. The components of the function include:
- \( 3^h \): This term represents exponential growth of the bacteria over time.
- \( -2h \): This term indicates a linear decrease in the number of bacteria colonies as time progresses.
- \( +20 \): This is a constant term that we need to analyze.

### Step 2: Calculate the initial number of bacteria
To understand what the constant 20 represents, we can find the value of \( C(h) \) when \( h = 0 \) (i.e., at the beginning of the experiment).

\[ C(0) = 3^0 - 2(0) + 20 \]

### Step 3: Simplify the expression
Now, simplify the expression:

\[ C(0) = 1 - 0 + 20 = 1 + 20 = 21 \]

### Step 4: Interpret the result
At \( h = 0 \), the number of bacteria colonies is 21. Since the function \( C(h) \) gives us the number of bacteria colonies after \( h \) hours, the constant term \( +20 \) can be interpreted as follows:

- The initial number of bacteria colonies at \( h = 0 \) is 21.
- Therefore, the number 20 represents one less than the initial number of bacteria colonies.

### Conclusion
Thus, the number 20 in the function \( C(h) \) represents one less than the initial number of bacteria in the colonies.

### Final Answer
The correct interpretation is:
**C: one less than the initial number of bacteria in the colonies.**

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