Question

Suppose elephant poaching reduces an initial animal population of 25,000 animals by 15% each year. 1. Find the rate of change.2. How many animals will be left in 10 years?

Answer 1

Initial animal population, P₀ = 25,000

1. Rate of change = 15% = 0.15

2. Animal left in 10 years?

To calculate the animals left in 10 years, we use the formula:

P(t) = P₀ (1 - r)^t in t years

t = 10, P₀ = 25,000, r = 15% = 0.15)

P₍₁₀₎ = 25000 (1 - 0.15)¹⁰

P₍₁₀₎ = 25000 (0.85)¹⁰

P₍₁₀₎ = 25000 (0.1969)

P₍₁₀₎ = 4922.50

Therefore, 4922.50 animals will be left in 10 years.