Question

The total number of roller coasters at the park for Years 3, 6, 9, and 12 is, respectively, 7, 13, 19, and 25. a) What is the initial number of roller coasters at the amusement park? Assume that the relationship between the two quantities is linear. b) Write a function to represent the situation.

Answer 1

Let the initial no. Of rollercoaster be x

Let no. Of rollercoaster set up every year be y

t be the no. Of years

x+ty=no. Of rollercoasters per year

After 3 years (t=3)

x+3y=7

t=6

x+6y=13

So solving these we get

x=1 & y=2

Thus initial no. Of rollercoaster=1

And the linear relationship is

No. Of rollercoaster after t years

N=1+2t