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We are given the following mathematical model for the costs of a family basket $ C(t) = P(1.02)^t $, where:

- $ P $ is the current price of the basket at $ t = 0 $ (which is \$150),
- $ t $ represents time in years, 
- 1.02 represents a 2% annual inflation rate.

The goal is to calculate the price after 10 years, i.e., $ C(10) $.

### Steps:

1. Use the formula for the price after $ t $ years: 
   \[
   C(t) = 150 \times (1.02)^t
   \]
   with $ t = 10 $.

2. Substitute and compute:
   \[
   C(10) = 150 \times (1.02)^{10}
   \]

Let me calculate that for you.The price of the family basket after 10 years will be approximately **$182.85**.

This matches the closest option, which is **$182.85**.

Would you like further clarification on any part of the process or more details?

Here are some related questions you might find interesting:
1. How does compound interest work in financial calculations?
2. How would the price change if the inflation rate were different?
3. Can inflation be modeled using other functions apart from exponential ones?
4. What is the formula for calculating inflation over multiple years?
5. How can inflation impact long-term financial planning?

**Tip:** Exponential growth is a key concept when calculating price changes due to inflation, as it compounds over time.

Si la tasa anual de inflación promedia en México será de 2% en los siguientes 10 años, los costos C(t) aproximados de la canasta familiar durante cualquier año en esa década estarán modelados por C(t) = P(1.02)^t, donde t es el tiempo en años y P es el costo presente. El precio de la canasta familiar (t = 0) es de $150. Calcule el precio que tendrá dentro de 10 años.

Learn how to calculate the price of a family basket in 10 years based on a 2% annual inflation rate. The problem involves using the exponential growth formula C(t) = P(1.02)^t to find the price after a decade, with the initial price of $150.

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