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You have been gotten a job offer and the company wants to start you out at
$45,000 and will give you a 5% raise every year. Write an equation you could use to
determine how much you would be making after x number of years.

Sagot :

I can tell you that 5% of 45,000 is 2250! so i think the equation would be something like 45,000 + 2250x

The equation that we would be making after x number of years is S(x) = 45000(1.05)^x where S(x) is the salary in xth year since the year of joining the job.

How to form mathematical expression from the given description?

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Let the initial income be P

Let the raise be of R% annually.

Then, after 1 year, it would become
[tex]P_1 = P + (R\% \: of \: P) =P + \dfrac{P}{100} \times R = P\left(1 + \dfrac{R}{100}\right)[/tex]

Now, after 1 more year(second year), we get:

[tex]P_2 = P_1\left(1 + \dfrac{R}{100}\right) = P\left(1 + \dfrac{R}{100}\right)\left(1 + \dfrac{R}{100}\right) = P\left(1 + \dfrac{R}{100}\right)^2[/tex]

After one more year(third year), we get:

[tex]P_3 = P_2\left(1 + \dfrac{R}{100}\right) = P_1\left(1 + \dfrac{R}{100}\right)^2 = P\left(1 + \dfrac{R}{100}\right)^3[/tex]

Similarly, on xth year, we get:

[tex]P_x = P\left(1 + \dfrac{R}{100}\right)^x[/tex]

This is the salary on xth year.

For this case, we're provided that:

  • P = $45,000
  • R = 5

Thus, we get:

[tex]P_x = P\left(1 + \dfrac{R}{100}\right)^x\\\\P_x = 45000(1 + 0.05)^x = 45000(1.05)^x = S(x) \: \rm (say)[/tex]

Thus, the equation that we would be making after x number of years is [tex]S(x) = 45000(1.05)^x[/tex] where S(x) is the salary in xth year since the year of joining the job.

Learn more about forming equations here:

https://brainly.com/question/11938672

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