Question

In the year 2000, the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function f(x) = 100(1.0153)x gives the population, in millions, x years after 2000. Using this model, in what year would the population reach 111 million? Round your answer to the nearest year.

Answer 1

Answer: The population reach 111 million in 2007.

Explanation:

In the year 2000, the population of Mexico was about 100 million, and it was growing by 1.53% per year.

At this growth rate, the function
`f(x) = 100(1.0153)^x` gives the population, in millions, x years after 2000.

Put f(x)=111 million.

Then,

`111=100(1.0153)^x\\\\\Rightarrow\ (1.0153)^x=(111)/(100)=1.11\\\\\Rightarrow (1.0153)^x=1.11`

Taking log on both the sides , we get

`x\log1.0153=\log1.11\\\\\Rightarrow\ x=(\log1.11)/(\log1.0153)=(0.045323)/(0.0066)=6.86712121212\approx7`

Hence, the population reach 111 million in 2007 (approx).