Question

You have a job as a teacher. Your salary for the first year is $37,185.

Answer 1

Answer:

a). Geometric sequence

b). $S_{t} =\ 37185(1+\frac{6}{100})^{(t-1)}$

c). $46945.21 will be the salary at the start of 5th year.

Step-by-step explanation:

My salary for the first year is $37185.

If I get an increase of 6% every year then the next year salary will be,

$S_{1}=\ 37185(1+\frac{6}{100})$

   = $39416.1

Similarly in the second year my salary will be

$S_{2}=\ 39416.1(1+\frac{6}{100})$

    = $41781.07

So the sequence becomes $37185, $39416.1 $41781.07.....

And there is a common ratio in each successive term 'r' = 1.06

a). Therefore, it's a geometric sequence.

b). Explicit formula for this sequence will be in the form of

$S_{t} =\ 37185(1+\frac{6}{100})^{(t-1)}$

Where t = duration in years

c). Salary at the start of 5th year,

$S_{(5)}=\ 37185(1+\frac{6}{100})^{5-1}$

$S_{(5)}=\ 37185(1.06)^{4}$

       = $46945.21