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You have a job as a teacher. Your salary for the first year is $37,185.
You will receive a 6% increase every year.
Part A Would an arithmetic or geometric sequence best model this situation?
Select a Value
Part B: What explicit formula models this situation?
Select a Value
Part C How much will your salary be at the start of your 5th year?
Select a Value

Respuesta :

Answer:

a). Geometric sequence

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

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,

[tex]S_{1}=\$37185(1+\frac{6}{100})[/tex]

   = $39416.1

Similarly in the second year my salary will be

[tex]S_{2}=\$39416.1(1+\frac{6}{100})[/tex]

    = $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

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

Where t = duration in years

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

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

[tex]S_{(5)}=\$37185(1.06)^{4}[/tex]

       = $46945.21

facundo3141592

By using a increasing exponential equation, we will see that:

  • a) Geometric sequence.
  • b)  y = $37,185*(1 + 0.06)^x
  • c)  $49,761

How to work with exponential equations?

We know that each year your salary increases by a fixed percentage of 6%, then your salary will be modeled with an exponential equation.

A) The sequences that have exponential behavior are the geometric ones, so this would be represented with a geometric sequence.

B) The general formula is:

y = A*(1 + r)^t

Where A is the initial amount and r is the percentage of increase in decimal form, then we can write:

y = $37,185*(1 + 0.06)^x

C) To get this we need to replace x by 5 in the above equation:

y = $37,185*(1 + 0.06)^5 = $49,761

If you want to learn more about exponential functions, you can read:

https://brainly.com/question/11464095

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