Evaluate the given function as required.

Calculate *N*(0) and *N*(18) if *N*(*t*) is as follows. (Round your answers to two decimal places.)

*N*(*t*) = 

12.44

0.03 + 0.55*t*
 

To evaluate the function \( N(t) = \frac{12.44}{0.03 + 0.55t} \) at \( t = 0 \) and \( t = 18 \), we substitute the values of \( t \) into the function.

### Step 1: Calculate \( N(0) \)
Substitute \( t = 0 \) into the function:

\[
N(0) = \frac{12.44}{0.03 + 0.55(0)}
\]

Simplifying:

\[
N(0) = \frac{12.44}{0.03}
\]

Now, divide:

\[
N(0) \approx 414.67
\]

### Step 2: Calculate \( N(18) \)
Substitute \( t = 18 \) into the function:

\[
N(18) = \frac{12.44}{0.03 + 0.55(18)}
\]

Simplifying:

\[
N(18) = \frac{12.44}{0.03 + 9.9}
\]

\[
N(18) = \frac{12.44}{9.93}
\]

Now, divide:

\[
N(18) \approx 1.25
\]

### Final Answer:
- \( N(0) \approx 414.67 \)
- \( N(18) \approx 1.25 \)

Would you like details or have any questions?  
Here are 5 related questions:
1. How would you calculate \( N(10) \) using the same function?
2. What happens to \( N(t) \) as \( t \) increases indefinitely?
3. How would you modify the function if the numerator changed from 12.44 to 20?
4. How does the function behave if \( t \) is negative?
5. Can this function represent a real-world scenario, such as decay over time?

**Tip:** When dealing with functions, always substitute the values carefully and ensure you follow the order of operations correctly.

Learn how to evaluate the function N(t) = 12.44 / (0.03 + 0.55t) at t = 0 and t = 18 with a step-by-step solution. This problem involves rational functions and requires basic algebraic manipulation. Suitable for high school students studying functions and algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation