+0  
 
0
39
2
avatar+648 

A mechanical engineer earned a yearly salary of $50,000 in 1990 and has averaged a 6.2% raise anually for the last 10 years and expects that this increase will continue.

 

a) Write an equation that models this situation. Let S=yearly salary and n=number of yrs. since 1990.

 

b) According to your equation, what was the engineer's salary in 1980?

 

c) How long will it take for the engineer's salary to reach $100,000?

 

d) Write a doubling time equation for this situation.

 
AdamTaurus  Dec 7, 2017
Sort: 

2+0 Answers

 #1
avatar+5552 
+1

A mechanical engineer earned a yearly salary of $50,000 in 1990 and has averaged a 6.2% raise anually for the last 10 years and expects that this increase will continue.

 

a)  Write an equation that models this situation.

     Let  S = yearly salary  and  n = number of years since 1990 .

 

when  n = 0 ,   S  =  50000

when  n = 1 ,   S  =  1.062 * 50000

when  n = 2 ,   S  =  1.062 * 1.062 * 50000

when  n = 3 ,   S  =  1.0623 * 50000

 

So...

 

S  =  1.062n  *  50000

 

b)  1980  =  1990  +  -10 ,  so our   n = -10  .

 

S  =  1.062-10  *  50000

S  ≈  27398

 

c)

 

100000   =   1.062n  *  50000          Divide both sides by  50000 .

2   =   1.062n                                 Take the  ln  of both sides.

ln 2   =   ln 1.062n

ln 2   =   n ln 1.062

ln 2 / ln 1.062   =   n

11.5   ≈   n

 

If it is a steady increase, it will take about  11.5  years after 1990 for the salary to reach 100,000 .

 

d)    I don't know what that is...sorry!!!

 
hectictar  Dec 8, 2017
edited by hectictar  Dec 8, 2017
edited by hectictar  Dec 8, 2017
 #2
avatar+79819 
+2

d. The doubling time, t,  is independent of any amount

 

So

 

2A  =  A (1.062)^t      divide both sides by  A

 

2 = 1.062^t      take the log of both sides

 

log 2  =  log (1.062)^t     and we can write

 

log (2)  =  t * log (1.062)     divide both sides by log (1.062)

 

log (2) / log (1.062)  = t    ≈ 11.52 yrs  ≈ 12 years   .i.e., it takes any starting amount about 12 years to double

 

 

cool cool cool

 
CPhill  Dec 8, 2017
edited by CPhill  Dec 8, 2017
edited by CPhill  Dec 8, 2017

15 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details