An amusement park's average daily attendance during its first year of
operation in 1988 was 2046 people. since the the average daily attendance ahs increased by about 115 people yearly. let (T) be the number of years since 1988. use function notation to write an equation giving the average daily attendance as a function of (T). then determine the average daily attendance in the year 2003.
Let T be the number of years since 1988.
N(T) = 115T + 2046
so 2003 ---> T = 15
N(15) = 115(15) + 2046 = 3771
To write an equation giving the average daily attendance as a function of (T), we need to find the initial value and the rate of change.
In this case, the initial average daily attendance in 1988 is given as 2046 people. The rate of change is stated as an increase of about 115 people yearly.
Let's denote the average daily attendance as A(T), where T represents the number of years since 1988.
Since the average daily attendance increased by 115 people each year, we can write the equation as:
A(T) = 2046 + 115T
To determine the average daily attendance in the year 2003, we need to find the value of T when T is the number of years since 1988.
The year 2003 is 2003 - 1988 = 15 years after 1988. So, we substitute T = 15 into the equation:
A(15) = 2046 + 115(15)
A(15) = 2046 + 1725
A(15) = 3771
Therefore, the average daily attendance in the year 2003 was 3771 people.