A study estimated how a person\'s social status (rated on a scale where 100 indi
ID: 2872899 • Letter: A
Question
A study estimated how a person's social status (rated on a scale where 100 indicates the status of a college graduate) depended upon income. Based on this study, with an income of i thousand dollars, a person's status is S(i) = 17.5(i 1)0.53. † Find
S'(21). (Round your answer to two decimal places.)
S'(21) = _____
Interpret your answer.
___At an income of $21,000 social status increases by this amount per additional $1000 of income.
___At an income of $21,000 social status decreases by this amount per additional $1000 of income.
___At an income of $21,000 social status does not change.
___At an income of $21,000 social status increases by this amount per additional $100 of income.
___At an income of $21,000 social status decreases by this amount per additional $100 of income.
Explanation / Answer
Answer:
With an income of i thousand dollars, a person's status is S(i) = 17.5(i 1)0.53
differentiate with respect to i, we get
S'(i) = (17.5)(0.53)(i 1)0.53-1
S'(i) = (17.5)(0.53)(i 1)-0.47
put i=21 we get
S'(21) = (17.5)(0.53)(21 1)-0.47
S'(21) = (17.5)(0.53)(20)-0.47
S'(21) = 2.27
(1) At an income of $21,000 social status increases by this amount per additional $1000 of income is
S(22) = 17.5(22 1)0.53
S(22) = 17.5(21)0.53
S(22)=87.86
But S(21)=85.62
Hence the social status is increased by 87.86-85.62=2.24.
(b) At an income of $ 21000, we have the social status of the person is S(21)=85.62 and S'(21)=2.27
(C) At an income of $21,000 social status increases by this amount per additional $100 of income is
S(21.1) = 17.5(21.1 1)0.53
S(21.1) = 85.84
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