Question

At the beggining of a population study, a city had 300,000 people. Each year since, the population has grown by 6.8%

Answer 1

Complete question: At the beginning of a population study, a city had 300,000 people. Each year since, the population has grown by 6.8%.
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.

To model this situation we are going to use the standard exponential grow function: $y=a(1+b)^t$
where
$y$ is the final population after $t$ years of exponential grow
$a$ is the initial population
$b$ is the grow rate in decimal form 
$t$ is the time in years 

We know form our problem that the initial population of the city at the beginning of the study was 300,000 people, so $a=300,000$. Now, to convert the grow rate to decimal form, we are going to divide the rate by 100%:
$b= \frac{6.8}{100}$
$b=0.068$
Now that we have all the values we need, lets replace them in our grow function:
$y=a(1+b)^t$
$y=300,000(1+0.068)^t$
$y=300,000(1.068)^t$

We can conclude that the function that shows the relationship between $y$ and $t$ is $y=300,000(1.068)^t$.