The population (in millions) of a certain island can be approximated by the function:

P(x)=50 (1.05)^x

Where x is the number of years since 2000. In which year will the population reach 200 million?

Question

The population (in millions) of a certain island can be approximated by the function:

P(x)=50 (1.05)^x

Where x is the number of years since 2000. In which year will the population reach 200 million?

anonymous · Answer

it would be 2028, right? or am i off?

wolf1728 · Answer

population = 50*(1.05)^x
population / 50  =  (1.05)^x
log (population / 50) = x * log (1.05)
log (population / 50) / log (1.05) = x
we need to know when population = 200,000,000 so according to the formula the population will equal 200:
log (200 / 50) / log (1.05) = x
0.6020599913 / 0.0211892991 = x
x = 28.4133981658 Years