For 1985 through 1996, the number, C (in thousands), of videos rented each year in Moose Jaw can be modeled by C= 0.069(t^3+4t^2+37t+600) where t=0 represents 1990. During which year are 60.4 thousand movies projected to be rented?

Could someone please show me the steps to this problem?

1 answer

You have the equation. Just solve for t:

C= 0.069(t^3+4t^2+37t+600)
60.4 = 0.069(t^3+4t^2+37t+600)
875.36 = t^3+4t^2+37t+600
t^3 + 4t^2 + 37t - 275.36 = 0

Cubics are hard to solve, but there are many online polynomial solvers. We get

t = 3.99, or just 4.

So, it looks like 1994 is the year you want.

Note: 4 is an exact root of

t^3 + 4t^2 + 37t - 276 = 0
which could have been found using trials of synthetic division.