One year after graduating from college, Sam earned $42,000. Each year, he earned $4000 more.
What function, written in sequence notation, models Sam’s earnings n years after graduating college?
The key here is which value is the constant:
In this problem the value that doesn't change yearly, meaning that its not multiplied with n in the function should be his base earning from which he earns 4000 more each year. We know that after one year, Sam earned 42k, so subtracting the one year that added 4k and we get a "base wealth" of 38k. We can eliminate any function that doesn't have 38,000: eliminating 3, 4.
We are left with options 1: a(n) = 4000n + 38,000 and 2: a(n) = 38,000n + 4000.
By looking at the functions, we can see that in option 2, with every additional year Sam acquires 38,000 more, rather than 4000 more as described in the problem. Therefore we can choose option 1: a(n) = 4000n + 38000.
To check, we can plug in 1 for n:
a(1) = (4000 * 1) + 38000
a(1) = 4000 + 38000
a(1) = 42000, just like in the problem description.