The average salary (in thousands of dollars) at a certain company for the first ten years of its existence can be approximated by the model S = 0.2t2 + 2.1t + 32.5, 0 t 10. How many years did it take for the average salary to reach $41,000? Round the answer to the nearest hundredth of a year.

3.12years

Step-by-step explanation:

Given the average salary (in thousands of dollars) at a certain company for the first ten years of its existence approximated by the model

S = 0.2t² + 2.1t + 32.5,

To calculate the years it take for the average salary to reach $41,000, we will substitute s = 41000 and calculate for t

41 = 0.2t² + 2.1t + 32.5

Multiply through by 10

410 = 2t²+21t+325

2t²+21t+325 = 410

2t²+21t+325-410= 0

2t²+21t-85 = 0

On factorizing:

t = -21±√21²-4(2)(-85)/2(2)

t = -21±√441+680/4

t = -21±√1121/4

t = -21+33.48/4

t = 12.48/4

t = 3.12

Hence the number of years to average hundredth of a year is 3.12years