We are given a model of passenger movements through an airport as: #y=592x^2-1002x+89401# where; #y# is passenger movement in thousands and #x# is years after 2008. Find (a) the passenger movement in 2015 and (b) the year passenger movements exceed 150m.?
2 Answers
a. 111,395 passengers
b. 2019
Explanation:
Okay, let's start off with part a.
If we want the number of passengers in 2015, we first need to find
Now, we can plug it into the equation:
(Obviously, you will need a calculator for this part!)
Let's move on to part b. Now, the problem gives us the value of
From here, there are three ways to solve this quadratic equation. You can factor it (too hard), use the quadratic equation (too hard), or graph it and find the zeros (complicated, but the best choice).
Here is our graph of
graph{592x^2-1002x-60599 [-114.3, 120, -52.8, 64.3]}
Obviously, there is more to this graph, but we only care about when the function is equal to 0 (when it crosses the x-axis). We can see there are two intersections,
Hope this helps!
See solutions below.
Explanation:
We are given the model:
Where;
and
(a) To find the passenger movement in 2015;
Hence,
(b) To find the year in which passenger movements exceed 150,000 thousand.
To find our year from 2008 when this occurs we could simply set
Let's round the model to hundreds of thousands by dividing through by 100 and rounding the coefficients.
To find the offset when passenger movement reaches 150,000k
For the pursose of our model we can assume this to be an equality.
Hence:
Applying the quadratic formula
We are only interested in the positive result.
Hence, our offset from 2008 is 11 years.
The passenger movements will exceed 150,000k in year