Solution: The population grows as \( 324 \times 2^{t/3} \), where \( t \) is time in years. We want the smallest \( k \) such that:

Sat, 02 May 2026 23:02:23 +0000

Title: Understanding Population Growth: The Case of \( 324 \ imes 2^{t/3} \) Introduction
Population growth is a key topic in demography, urban planning, and environmental studies. One population model describes growth using the formula \( P(t) = 324 \ imes 2^{t/3} \), where \( P(t) \) represents the population at time \( t \) in years, and \( 324 \) is the initial population. This exponential model reveals how quickly populations expandÃƒÂ¢Ã‚Â€Ã‚Â”especially under favorable conditions. In this article, we explore the meaning of this function and highlight the smallest integer \( k \) such that population levels remain valid and meaningful over time. --- ### The Mathematics Behind Population Growth