precalculus

Question

In 2008, the population of Kenya was approximately 38.3 million and was growing by 2.64% per year, while the population of Sudan was approximately 41.3 million and growing by 2.24% each year. If these trends continue, when will the population of Kenya match the population of Sudan?

Answer 1

38.3(1.0264)^t = 41.3(1.0224)^t

1.0264^t ≈ 1.0783(1.0224)^t

ln 1.0264^t ≈ ln [ 1.0783(1.0224)^t ]

ln 1.0264^t ≈ ln 1.0783 + ln 1.0224^t

t ln 1.0264 ≈ ln 1.0783 + t ln 1.0224

0.0261t ≈ 0.075 + 0.0221t

0.004t = 0.075

t ≈ 18.75

Answer 2

using Logs: 19.3 y