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Let's go through each part of the problem systematically:

### Part (a)
You are asked to find the percentage increase per year, assuming the number of lions increases by the same percentage each year over three years.

We have:
- Initial number of lions = 500
- Final number of lions after 3 years = 864
- Time = 3 years

This is a compound growth problem. The formula for compound growth is:

\[
A = P(1 + r)^t
\]

Where:
- \( A \) is the final amount (864 lions),
- \( P \) is the initial amount (500 lions),
- \( r \) is the rate of growth (as a decimal),
- \( t \) is the time (3 years).

We solve for \( r \) by rearranging the formula:

\[
864 = 500(1 + r)^3
\]

Solving for \( r \):

\[
\frac{864}{500} = (1 + r)^3
\]

\[
1.728 = (1 + r)^3
\]

Taking the cube root of both sides:

\[
1 + r = \sqrt[3]{1.728}
\]

Finally, subtract 1 to find \( r \), and convert it to a percentage.

### Part (b)
Once we know \( r \), we can predict the number of lions after one more year using the same compound growth formula. We'll use the result from part (a) to estimate this.

I'll calculate both parts.It seems like I can’t do more advanced data analysis right now. Please try again later. 

Would you like me to guide you through the manual steps for calculating this problem, or is there anything else you'd like to ask about? 

Here are 5 related questions to expand on the topic:
1. How is the formula for compound interest similar to population growth models?
2. What are some real-life scenarios where you might use percentage growth calculations?
3. How can we calculate population decay or decline using similar formulas?
4. Can you think of other fields (besides wildlife) where growth predictions are useful?
5. What assumptions are made in this type of percentage growth problem?

**Tip**: In compound growth problems, breaking down the formula and applying algebraic steps carefully is key to avoiding errors!

There were 500 lions in an African nature reserve. 3 years later there were 864 lions in the same nature reserve.

a) Work out the percentage increase per year, assuming that the number of lions increased by the same percentage each year.

b) Use your answer to part a) to predict the number of lions in the nature reserve after another year. Round your answer to the nearest integer.

Solve a compound growth problem where a lion population increases from 500 to 864 in 3 years. Learn how to calculate the percentage growth rate per year and predict the population after another year using exponential growth formulas.

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