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

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: 
where
is the final population after years of exponential grow
is the initial population
is the grow rate in decimal form 
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 . Now, to convert the grow rate to decimal form, we are going to divide the rate by 100%:


Now that we have all the values we need, lets replace them in our grow function:




We can conclude that the function that shows the relationship between  and  is .

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