Between 2008 and 2012, the revenue obtained from digital music albums downloads, r, in millions of dollars, in the United States increased by approximately 132 million dollars per year. In 2010, the digital music revenue in the U.S. was about 872 million dollars. If t represents years since 2008, which of the following best models the situation for 0 ≤ t ≤ 4?
1) r(t) = 132t
2) r(t) = 132t + 608
3) r(t) = 132t + 872
4) r(t) = 132t + 1136
Solution: Choice B is correct.
Since the revenue increases by 132 million dollars per year, the rate of change is constant.
Therefore, we can form a linear function to solve the problem.
Now, we are also given that when t=2, r=872.
Therefore, using slope point form of a line we have,
r – 872 = 132 (t – 2)
Or r = 132 t + 608.
Since in 2010 (t=2), the revenue given is 872 million dollars.
We can substitute t=2 in the options given and see for which option r(2) = 872.
Clearly only choice B satisfies the same.