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To solve the problem, we need to determine the number of infected people after 3 days using the given exponential growth formula:

\[
C = I(1 + r)^t
\]

where:
- \( I = 5000 \) (initial number of infected people),
- \( r = 0.2 \) (growth rate),
- \( t = 3 \) (time in days).

Substituting the values into the formula:

\[
C = 5000 \times (1 + 0.2)^3
\]

Now, let's calculate it step-by-step:

\[
C = 5000 \times (1.2)^3
\]

Calculating \( (1.2)^3 \):

\[
(1.2)^3 = 1.2 \times 1.2 \times 1.2 = 1.728
\]

Then, multiply by 5000:

\[
C = 5000 \times 1.728 = 8640
\]

Thus, the number of infected people after 3 days is:

**8640**

### Would you like more details or have any questions?

### Related Questions:
1. How would the result change if the growth rate \( r \) was 0.1 instead?
2. What would be the number of infected individuals after 5 days?
3. How can we adjust the formula if the growth rate changes daily?
4. What would be the effect of reducing the initial number of infected individuals to 3000?
5. How can we model this scenario if the growth rate is not constant?

**Tip:** Understanding the exponential growth formula is essential for predicting trends in rapidly changing populations, such as viral infections.

La población de personas infectadas por un virus en una ciudad actualmente es de 5000 personas. Determine la cantidad de personas infectadas al cabo de 3 días, si se sabe que el número de personas infectadas crece exponencialmente según la siguiente fórmula: C = I(1 + r)^t. Donde r = 0.2, I: número inicial de personas infectadas, t: número de días transcurridos.

Calculate the number of people infected by a virus after 3 days using the exponential growth model. With an initial population of 5000 infected, a growth rate (r) of 0.2, and the formula C = I(1 + r)^t, this problem covers important algebraic concepts. Suitable for Grades 8-10.

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