Answer to Question #270309 in Financial Math for Zor

Question

• Suppose you are being interviewed for your dream job. The pay is tricky and there's also a catch: the job is only for 5 months.
• Your future boss tells you that the first week's pay will be $10 (not per hour, the whole week is $10!)
• Concerned about your reaction, your future boss adds that your week 4 salary will be $100 (again, not per hour).
• Knowing how valuable you would be to the company and before you storm out of the office the boss mentions that the pay increases exponentially every week. 
• Now... would you take this job?

1. Find the model that describes this salary situation using the variable "t" as the number of weeks.
2. Week #1 corresponds to "t=0". Week #2 corresponds to "t=1", etc... How much will you get paid in Week 3?
3. For simplicity, assume that a month has exactly 4 weeks. How much will you get paid during the last week.

Answer 1

1.

let x be salary per week, then:

$x(t)=10$ for $0\le t\le3$

$x(t)=100$ for $t=4$

$x(t)=100(1+r)^{t-4}$ for $5\le t\le20$

where r is growth rate

2.

$x(3)=\$10$

3.

$x(20)=100(1+r)^{16}$