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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

Respuesta :

Aliwohaish12
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:

The population would reach [tex]111[/tex] million in next [tex]7[/tex] years

Step-by-step explanation:

The initial population of Mexico was [tex]100[/tex] million

The growth rate of the population is [tex]1.53[/tex] %per year

Then the future population of Mexico is given by

[tex]P = P_{0} (1 +r)^t\\[/tex]

Where P = future population after t years

[tex]P_{0} =[/tex] initial population

t = time period in years

Substituting the given vales in above equation we get

[tex](111 *10^6) = (100*10^6) (1+0.0153)^t\\(1+0.0153)^t = \frac{111 *10^6}{100*10^6} \\(1+0.0153)^t = 1.11[/tex]

Taking log on both sides we get

[tex]t * log (1.0153) = log (1.11)\\t = \frac{log (1.11)}{log (1.0153)} \\t = 6.87[/tex]

≈ [tex]7[/tex] years

The population would reach [tex]111[/tex] million in next [tex]7[/tex] years

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