Question

Puerto Rico saw a population decrease of 11.8% since 2010. If the population of Puerto Rico in 2010 was approximately 3.72 million people, write an exponential equation to model Puerto Rico's population (in millions) after t years.

a) P(t)=3.72×e^−0.118t
b) P(t)=3.72×(1−0.118)^2
c)P(t)=3.72×(1+0.118)^2
d)P(t)=3.72×(1−0.118)^−t

Answer 1

The correct exponential equation to model Puerto Rico's population decrease is P(t)=3.72×(1−0.118)^t, which accounts for an 11.8% annual decrease in population since 2010.

Step-by-step explanation:

The question at hand involves determining the correct exponential equation to model Puerto Rico's population decrease over time. Given the percentage decrease and the initial population, we can figure out which equation is accurate.

Since the population is decreasing by 11.8% since 2010, the correct representation would need to subtract this decrease from 1 to show a reduction over time. Therefore, using t for the number of years since 2010, the correct formulation for P(t), the population at time t, in millions, is given by:

P(t)=3.72×(1−0.118)^t.

This equation represents an exponential decay model where the base of the exponent, (1−0.118), signifies a decrease of 11.8% per year. The other options either mistakenly use an increase, apply the percentage decrease incorrectly, or relate to other models not pertinent to the scenario.