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= (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`.