Question

from 2005 to 2015 a population of p lions is modeled by the equation p=1,500 (0.98) t , where t is the number of years since 2005

Answer 1

It means the lion population is modeled exponentially by
p(t) = 1500·(0.98)^t, with t = years since 2005.

Interpretation:
- Initial population (2005, t = 0): p(0) = 1500 lions.
- Growth factor each year: 0.98 → a 2% decline per year.

Common values:
- In 2015 (t = 10): p(10) = 1500·(0.98)^10 ≈ 1500·0.81707 ≈ 1226 lions.
- In 2010 (t = 5): p(5) ≈ 1500·(0.98)^5 ≈ 1356 lions.
- Time to halve (p = 750): t = ln(0.5)/ln(0.98) ≈ 34.3 years → about year 2039.

Let me know if you want other years, a table, or a plot.