Question

At the beginning of a population study, a city had 330,000 people. Each year since, the population has grown by 2.7% let t be the number of years since start of the study. Let y be the city's population.

Answer 1

The population of a city at the beginning of a study is 330,000

Let the first term, y = 330000

If there is an increase of 2.7% yearly, the population for the following year (2nd year) will be

$y_1=\frac{2.7}{100}\times330000=338910$

The population the following year is 338910

Since there is an increase of 2.7% every year,

The common ratio, r, is

$\begin{gathered} r=\frac{338910}{330000}=1.027 \\ r=1.027 \end{gathered}$

Hence, the exponential relationship between y and t is

$y_t=330000(1.027)^t^{}$