Rena has been offered entry-level positions with two firms.
Firm A offers a starting salary of $40 000 per year, with a $2000 per year increase guaranteed each subsequent year.
Firm B offers a starting salary of $38 500, with a 5% increase every year after that.
a)After how many years will Rena earn the same amount at each firm?
b) At which firm will Rena earn more after
i) 10 years ii) 20 years
Firm A's salaries increase linearly, (they form an arithmetic sequence)
Firm B;s salaries increase exponentially, (they form a geometric sequence)
SA = 2000t + 40000, where t is number of years after starting
SB = 38500(1.05)^t
a) you would have to solve
38500(1.05^t = 40000 + 2000t
385(1.05)^t = 400 + 20t
I would just try a few values of t
t Left-side RS
5 491 500
8 569 560
7 542 540
9 597 580
What is your conclusion?
for b) just sub t = 10 and t = 20 into both equations.
To find the number of years it will take for Rena to earn the same amount at each firm, we need to set up an equation by equating the salaries at Firm A and Firm B.
a) Let's assume x represents the number of years.
For Firm A:
Salary = $40,000 + $2,000 * x
For Firm B:
Salary = $38,500 * (1 + 0.05)^x
Now, we can set up the equation by equating the salaries:
$40,000 + $2,000 * x = $38,500 * (1 + 0.05)^x
To solve this equation, you can either use trial and error by plugging in different values for x until you find the solution, or you can use a graphing calculator or software to find the point of intersection.
b) To determine which firm Rena will earn more after 10 years and 20 years, we need to calculate the salaries for each firm at these time points.
For Firm A after 10 years:
Salary = $40,000 + $2,000 * 10
For Firm B after 10 years:
Salary = $38,500 * (1 + 0.05)^10
Compare the two salaries to determine which one is higher.
For Firm A after 20 years:
Salary = $40,000 + $2,000 * 20
For Firm B after 20 years:
Salary = $38,500 * (1 + 0.05)^20
Again, compare the two salaries to determine which one is higher.
By comparing the salaries at each time point, you can determine which firm Rena will earn more from after a specific number of years.