The marine biologist introduces a genetically enhanced coral strain into a reef. The population grows exponentially: \( P(t) = 150e^{0.1t} \), where \( t \) is in years. What is the population after 5 years, to the nearest whole coral colony?

["Content:\nScientists in marine ecology have taken a groundbreaking step in coral reef restoration by introducing a genetically enhanced coral strain capable of rapid growth. Using a carefully optimized strain, researchers predict a powerful recovery trajectory, with the coral population modeled by the exponential function ( P(t) = 150e^{0.1t} ), where ( t ) represents time in years.", "To understand the actual size of the reef population after five years, scientists substitute ( t = 5 ) into the equation:", "[\nP(5) = 150e^{0.1 \ imes 5} = 150e^{0.5}\n]", "Using ( e^{0.5} \approx 1.6487 ), we calculate:", "[\nP(5) \approx 150 \ imes 1.6487 = 247.305\n]", "Rounding to the nearest whole coral colony, the population reaches approximately 247 colonies after five years. This exponential growth underscores the promise of genetically enhanced corals in revitalizing damaged marine ecosystems and accelerating reef recovery.", "Early field observations suggest high survival rates and rapid colonization, making this strain a powerful tool in combating coral bleaching and habitat loss worldwide. By combining science with conservation, marine biologists are forging a hopeful future for some of Earth’s most vital ecosystems.", "Stay tuned for updates on how these enhanced corals continue to transform reef resilience in the years ahead."]









