S\'(22)= _______________ Interpret your answer. Select on of the options below.
ID: 2856970 • Letter: S
Question
S'(22)= _______________
Interpret your answer. Select on of the options below.
__________ At an income of $22,000 social status increases by this amount per additional $1000 of income.
__________ At an income of $22,000 social status decreases by this amount per additional $1000 of income.
__________ At an income of $22,000 social status does not change.
__________ At an income of $22,000 social status increases by this amount per additional $100 of income.
__________ At an income of $22,000 social status decreases by this amount per additional $100 of income.
Explanation / Answer
Given function is S(i)=17.5(i-1)0.53 . For finding S' (22), find S' (i) first and then plug in i=22 to get S'(22). Accordingly, S'(i) = 17.5 (0.53)(i-1)0.53-1 =9.275 (i-1)-0.47 = 9.275/ (i-1)0.47. This expression shows the rate of change of social status with respect to i. Now plug in i=22 to get S'(22)
S'(22)= 9.275/ 21(0.47) =9.275/4.1825= 2.2175 This is the rate of change of social status at i= 22
Now looking at S'(i) expression worked out above,it shows that if i inceases from 22 to 23 or more,that is if the income increases by $1000 or more, the term in the denominator would be greater and this would make S'(i) lesser. This means that although social status would increase, the rate at which it would increase would be less or slow. For example at i=22 that is income of $22000, S(22)= 87.86, at i=23, S(23)= 90.05, Like wise for i=24, S(24)=92.20 and for i=25, S(25)=94.30.and so on. It can thus be observed that when i increases from 22 to 23, the change is 2.19, but when i increases from 23 to 24, the change is 2.05. When i ncreases to 25, the increase is now only 1.83 from the previous level. This shows that as income increases, the social status although increases, the rate of change becomes slower.
Hence 1st option seems to be the correct one.
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