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The problem provides an exponential model for the growth of the kiwi population, where:

\[
K = 100 \times (1.015)^t
\]

Here, \(K\) is the number of kiwis, and \(t\) is the number of months since the stoat control program started.

The question asks when the number of kiwis and stoats will be equal. However, there is no information given about the stoat population, such as its current size or growth model, which would be necessary to solve this problem. Usually, a stoat population model would either be a constant value or follow its own equation, such as exponential decay (if the population is being controlled).

Do you have any information on the stoat population growth or decline? If you could provide it, I can then solve for the number of months where the populations will be equal. 

Alternatively, if this information is not provided, it could be an assumption-based question, and I can guide you through that as well.

Would you like to clarify or upload any additional information?

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Here are 5 related questions to expand this:

1. What are the possible models that could represent the stoat population?
2. How does exponential growth compare to linear growth in wildlife populations?
3. What impact does a small increase in the growth rate (such as 1.015) have over time?
4. What are the key factors affecting the balance between predator and prey populations in controlled environments?
5. How does the exponential growth model change if the initial population was different?

**Tip**: When solving problems with population growth models, always double-check whether each population is growing or shrinking, as it directly impacts the solution approach.

With less stoats, the kiwi population on the island grows faster. It can be modelled by K = 100 x (1.015)^t where K is the number of kiwis and t is the number of months since the stoat control programme was started. After how many months would the numbers in the kiwi and stoat populations be the same if the programme continued?

Explore how to determine when the kiwi and stoat populations on an island would be equal using exponential growth models. This problem uses the exponential growth formula to model the kiwi population's increase over time.

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