The average total salaries for players in the National Basketball Association, S
ID: 3122284 • Letter: T
Question
The average total salaries for players in the National Basketball Association, S(t), have been shown to follow the function
S(t) = 161.4 (1.169)t
where t is the number of years since 1980 and S(t) is given in thousands of dollars. If this pattern continues, in what year did or will the average total salary for NBA players reach S = 180.000 thousand dollars, or $180 million dollars?
1998
2010
2024
2049
2075
5 log 16 – log 2 =
19 log 2
15 log 2
4 log 8
5 log 14
4 log 14
3 ln e3 + 4 ln e2 =
14
17
25
35
43
17
25
35
43
On the day his daughter is born, Lorenzo invests $2,500 in a rate money market rate account guaranteed to grow at 2.4%. If he leaves the investment to compound, how long will it take for the value of the account to double?
10.2
12.1
20.3
29.2
30.2
1998
b.2010
c.2024
d.2049
e.2075
Explanation / Answer
b) 5 log 16 – log 2 :
5 log (2)^4 - log 2
20 log 2 - log 2
log 2 (20 - 1)
19 log 2
c) 3 ln e^3 + 4 ln e^2
3*3 ln e + 4 * 2 ln e
9 ln e + 8 ln e
17 ln e
ln e = 1
thus , 17 is the answer
d) The rule number (e.g., 72) is divided by the interest percentage per period to obtain the approximate number of periods (usually years) required for doubling.
Thus, 72/2.4 = 30 so, approx 30.2 years
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