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 118 million? Round your answer to the nearest year.​

Answer 1

Answer:

11 years

Step-by-step explanation:

Set the function f(x) = 100(1.0153)^x = to 118 and solve for x:

100(1.0153)^x = 118

Taking the natural logarithm of both sides, we get:

ln 100 + x ln 1.0153 = ln 118

Then x ln 1.0153 = ln 118 - ln 100, or

                           = 4.7707 - 4.6052

    ... which leads to:

                                4.7707 - 4.6052

                         x = ---------------------------   =  11 years (rounded up from 10.888 )

                                     0.0152