Stephanie is organizing the seating arrangements for a concert in her local park. The first row’s seats are modeled by the function f(x) = 15. To give everyone a good view, each row must have four more seats than the row before it. The number of additional seats a row has is modeled by the function s(x) = 4(x – 1).
Explain to Stephanie how to create an equation to predict the number of seats in any row. Describe how to determine the number of seats in the 40th row. Use complete sentences.
Solution:-
seats in firs row f(x) = 15
number of additional seats are s(x) = 4(x-1)
equation of total number of seats
h(x) = g(x) + s(x)
h(x) = 15+4(x-1)
h(x) = 15 + 4x -4
h(x) = 4x + 11 …..(1)
here x is denoting the xth row.
to find the number of seats in the 40th row , we have to put x=40 in the equation(1)
h(40) = 4*40 + 11
h(40) = 160+11 = 171
So there are 171 seats in the 40th row.