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

111=100(1.0153)^x
Solve for x
X=log(111÷100)÷log(1.0153)
X=6.9years round the answer
X=7 years
So in what year
2000+7=2007
In the year 2007

Answer 2

The population would reach
`111` million in next
`7` years

Explanation:

The initial population of Mexico was
`100` million

The growth rate of the population is
`1.53` %per year

Then the future population of Mexico is given by

`P = P_(0) (1 +r)^t\\`

Where P = future population after t years

`P_(0) =` initial population

t = time period in years

Substituting the given vales in above equation we get

`(111 *10^6) = (100*10^6) (1+0.0153)^t\\(1+0.0153)^t = (111 *10^6)/(100*10^6) \\(1+0.0153)^t = 1.11`

Taking log on both sides we get

`t * log (1.0153) = log (1.11)\\t = (log (1.11))/(log (1.0153)) \\t = 6.87`

≈
`7` years

The population would reach
`111` million in next
`7` years