Answer:
Step-by-step explanation:
Given, Annual passenger revenue for the years 1980 to 2000 id=s modeled with the formula [tex]R=-40|x-11|+990[/tex].
Here, [tex]R[/tex] is the annual revenue in millions of dollars, [tex]x[/tex] is the number of years since January 1, 1980.
Revenue in a year was $ 790 million.
So, [tex]R=790\\-40|x-11|+990=790\\40|x-11|=200\\|x-11|=5\\x-11=5\text{ (or) }x-11=-5\\x=16\text{ (or) }x=6[/tex]
So, after 6 yrs and 16 yrs from January 1, 1980, the Passenger revenue equals $ 790 million.
∴ Passenger revenue equals $ 790 million in 1986 and 1996.
Solving the absolute value equation, it is found that the passenger's revenue was of $790 million in 1986 and in 1996.
The solution of the absolute value equation [tex]|x| = a[/tex] is given by: [tex]x = a[/tex] or [tex]x = -a[/tex].
In this problem, the revenue in x years after 1980, in millions of dollars, is given by:
[tex]R(x) = -40|x - 11| + 990[/tex]
The passenger's revenue is of $790 million when:
[tex]R(x) = 790[/tex]
Then:
[tex]790 = -40|x - 11| + 990[/tex]
[tex]-40|x - 11| = -200[/tex]
[tex]|x - 11| = \frac{-200}{-40}[/tex]
Negative divided by negative is positive, thus:
[tex]|x - 11| = 5[/tex]
Which means that:
[tex]x - 11 = 5 \rightarrow x = 16[/tex]
Or
[tex]x - 11 = -5 \rightarrow x = 6[/tex]
Thus, the passenger's revenue was of $790 million in 1986 and in 1996.
A similar problem is given at https://brainly.com/question/24514895
