The formula shown in the image is used to model exponential growth. Let's break it down:

Future Amount (A) = I(1 + r)ᵗ,
where:

• I is the initial number of rabbits (10 in this case),
• r is the growth rate (100% increase every month, so r = 1),
• t is the time in months (4 months in this case).

Substituting the values:

$A = 10(1 + 1)^4 = 10(2)^4$ Now calculate: $A = 10 \times 16 = 160$

Thus, the number of rabbits on the farm after 4 months will be 160 rabbits.

Would you like more details or have any questions?

Related Questions:

1. What if the growth rate was 50% per month instead of 100%?
2. How would the population change after 6 months instead of 4?
3. How does exponential growth differ from linear growth in this context?
4. What would happen if the initial population was doubled to 20 rabbits?
5. How can this model be adjusted for a non-constant growth rate?

Tip: Exponential growth can lead to very rapid increases in populations or quantities, making it a powerful tool for modeling real-world phenomena!