Respuesta :
Answer:
The equation that can be used to find the tuition y for x years after 2000 is:
[tex]y=24090x-3590[/tex]The tuition in 2020 is estimated to be $478,210
Explanation:
In 2000, the tuition was $20,500
In 2018, the tuition was $454,120
SInce x is the year since 2000, and y is the tuition, we want to write an equation that can be used to find the tuition y for x years after 2000
The equation is linear, as indicated at the end of the question: y = mx + b
The first term is 20500 in 2000
The last term (19th term) is 454120 in 2018
We have the nth term of a sequence to be:
[tex]T_n=a+(n-1)d[/tex]where a is the first term, and d is the common difference.
We need to know the common difference
[tex]\begin{gathered} 454120=20500+(19-1)d \\ \\ 454120-20500=18d \\ \\ 433620=18d \\ \\ d=\frac{433620}{18}=24090 \end{gathered}[/tex]Knowing the common difference, we now have the equation:
[tex]y=24090(x-1)+20500[/tex]OR
[tex]y=24090x-3590[/tex]This is in the form :
[tex]\begin{gathered} y=mx+b \\ \\ \text{where m = 24090, and b = -3590} \end{gathered}[/tex]Now, to estimate the tuition at this college in 2020, because this is 20 years after year 2000, we have x = 20
Using this in the last equation, we have:
[tex]\begin{gathered} y=24090(20)-3590 \\ \\ =481800-3590 \\ \\ =478210 \end{gathered}[/tex]The tuition in 2020 is estimated to be $478,210
