Question

At the beginning of a population study, a city had 390,000 people. Each year since, the population has grown by 7.3% . Let t be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and t .

Answer 1

T=number of years since start of the study.
y=city´s population.

first year:
y=390,000+0.073(390,000)=390,000(1+0.073)    (=418470)

Second year:
y=(390,000(1+0.073)  + 0.073(390,000(1+0.073) =
 =390,000(1+0.073) (1+0.073)
=390,000(1+0.073)²
  (≈449,018.31)

Third year: if you calculate it you would have:
y=390,000(1+0.073)³

Fourth year: if you compute it you would have:
y=390,000 (1+0.073)⁴

t th year:
y=390,000(1+0.073)^t

Answer: y=390,000(1+0.073)^t