https://file.aiquickdraw.com/mathbot/file/1727927286803zwfzfhrc.jpg

Solve step by step and talk in first person be very specific

The given problem asks us to calculate the number of infected passengers after one week, where the number of infected passengers is modeled by the function:

\[
A(t) = 3e^{0.35t}
\]

where \( t \) is the number of days since the first diagnosis, and we are asked to find \( A(t) \) after one week (7 days). I will now go through this step-by-step.

### Step 1: Set \( t = 7 \)
Since we're calculating the number of infected passengers after one week, \( t = 7 \) days.

\[
A(7) = 3e^{0.35 \times 7}
\]

### Step 2: Simplify the exponent
Let's simplify the exponent first:

\[
0.35 \times 7 = 2.45
\]

Now, the equation becomes:

\[
A(7) = 3e^{2.45}
\]

### Step 3: Calculate \( e^{2.45} \)
Using the value of \( e \approx 2.718 \), we can calculate \( e^{2.45} \):

\[
e^{2.45} \approx 11.58
\]

### Step 4: Multiply by 3
Now, multiply this result by 3 to get the number of infected passengers:

\[
A(7) = 3 \times 11.58 \approx 34.74
\]

### Step 5: Round to the nearest whole number
Rounding 34.74 to the nearest whole number gives:

\[
A(7) \approx 35
\]

### Final Answer:
After one week, approximately **35 passengers** will be infected.

---

Do you want any additional details on this process, or would you like me to explain a specific step further?

Here are 5 related questions to expand your understanding:

1. What is the significance of the exponential growth function in modeling infections?
2. How would the result change if the infection rate (0.35) were higher or lower?
3. How can you calculate the number of infected passengers after 10 days instead of 7?
4. How does rounding affect accuracy in real-life applications of mathematical models?
5. What would happen to the model if the base value (3 passengers) increased?

**Tip:** Exponential functions like this are often used to model population growth, radioactive decay, and spread of diseases because they capture the accelerating nature of these processes.

After the outbreak of a contagious virus on a cruise ship, epidemiologists find that the number of infected passengers is represented by A(t) = 3e^0.35t, where t represents the number of days since the first diagnosis. How many passengers will be infected after one week? Round your answer to the nearest whole number.

Learn how to calculate the number of infected passengers using the exponential growth model A(t) = 3e^(0.35t). In this example, after one week (7 days), we solve for the number of infected passengers. This problem covers key concepts of algebra and exponential growth, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation