word problem?

Question

The annual income "i" (in dollars) that a (MIT) graduate can expect to earn upon graduation can be modeled by the equation i(j)=418j^1.62+30,000 where j is the number of job offers they receive within one month of receiving their diploma. The number of job offers can be modeled by j(h)=0.6h where h is the number of hours spent studying per week. 1. Find and simplify i(j(h)) 2. Evaluate i(j(30)) 3. Explain the meaning of i(j(30))

Answer 1

i(j) = 418*j^1.62 + 30000

 

j(h) = 0.6*h 

 

To find i(j(h)), start with the equation for i(j) and replace every j with j(h) = 0.6*h

 

i(j(h)) = 418*(0.6h)^1.62 + 30000

         = 418*(0.6)^1.62 *h^1.62 + 30000

         = 418*(0.437)*h^1.62 + 30000

         = 182.666*h^1.62 + 30000

 

i(j(30)) = 182.666*(30)^1.62 + 30000

           = 182.666*247.136 + 30000

           = 45143.34 + 30000

           = 75143.34

 

i(j(30)) is the annual income in dollars that a MIT graduate who spends 30 hours per week studying can expect to earn upon graduation.