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.

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