+895 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.
+9479 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!!!
+129852 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
