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The given formula for the number of seals on the island is:

\[
P = 5200 \times 1.02^t
\]

Where:
- \( P \) is the number of seals at time \( t \) (in years).
- \( t \) is the number of years after the start of 2015.
- The factor \( 1.02 \) represents the annual growth rate.

The formula can be written in the form \( P = 5200 \times (1 + r)^t \), where \( r \) is the growth rate. In this case, the base \( 1.02 \) indicates an annual growth factor of \( 1 + r = 1.02 \).

Thus, the annual growth rate \( r \) is:

\[
r = 0.02 = 2\%
\]

### Final Answer:
The annual percentage increase in the number of seals on the island is **2%**.

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would you calculate the number of seals in 2020 using the formula?
2. What does the constant 5200 represent in this formula?
3. How does changing the value of \( 1.02 \) affect the population growth?
4. What happens to the population after 10 years, based on this growth rate?
5. How would you determine how many years it takes for the seal population to double?

**Tip**: Growth factors like 1.02 can be used to model many real-world processes, from population growth to interest rates. Understanding how the base influences growth helps with various types of exponential modeling.

An estimate for the number of seals on an island is given by the formula P = 5200 × 1.02^t where P is the number of seals t years after the start of year 2015. Write down the annual percentage increase in the number of seals on the island.

Understand how to calculate the annual percentage increase in the number of seals on an island using the exponential growth formula P = 5200 × 1.02^t. This problem explores exponential growth and percentage increase, suitable for students in Grades 9-12.

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