Question

laire started a new job in the year 2000. every year, her boss evaluates her work and adjusts her salary based on her performance. claire's annual salary tyears after 2000 can be modeled by the following function. c(t) = $40,000+ $1,000ln(t + 1)declan also started a job in the year 2000. every year, his boss evaluates his work and adjusts his salary based on his performance. declan's annual salary t years after 2000 can be modeled by the following table.$45,000 $45,623.83 $45,988.75 $46,247.66 $46,448.49which employee had the greater average rate of change in pay between 2001 and 2004? a) claire b claire and declan had the same average rate of change in payc) this cannot be determined from the given informationsd) declan​

Answer 1

Answer:

  Claire

Step-by-step explanation:

The change in Claire's salary over the 3-year period from 2001 to 2004 was ...

  (40000+1000(ln(1+4))) -(40000+1000(ln(1+1))) = 1000(ln(5)-ln(2)) = 916.29

The change in Declan's salary over the same 3-year period is ...

  46,448.49 -45,623.83 = 824.66

Since the change in Claire's salary is greater, the average rate of change for the period is greater for Claire's salary.

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The attachment shows the salaries for the two employees, and it shows Claire's salary curve adjusted upward so its rate of change can be directly compared to that for Declan.