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ngozi earns $24000 in salary in the first year she works as an interpreter. each year, she earns a 3.5% raise.

write a function that ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter

Respuesta :

CastleRook
Given that the current salary for Ngozi is $24000 and she earns 3.5% raise yearly, the function that will represent her salary in t years will be:
A=P(1+r)^t
where:
A=future amount
P=principle
r=rate
t=time 
thus plugging in the values we shall have:
s(t)=24000(1+3.5/100)^t
s(t)=24000(1.035)^t
thus the answer is:
s(t)=24000(1.035)^t

You can use the fact that raise is done on the previous years salary.

The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by

[tex]S = 24000 \times (1.035)^t[/tex]

How to calculate the final salary if increment is done per year on previous year's salary?

Let the initial salary was P = $24000

After 1 year, her salary increased by R = 3.5% which, thus,

Total salary = P + increment = [tex]P + P \times \dfrac{R}{100} = P(1 + \dfrac{R}{100}) = P_1 (say)[/tex]

After 1 more year, new salary will be

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

Similarly going on, we get

[tex]P_t = P(1 + \frac{R}{100})^t[/tex] = S (say)

Putting values of P and R, we get

[tex]S = 24000(1 + \frac{3.5}{100})^t = 24000 \times (1.035)^t[/tex]

Thus,

The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by

[tex]S = 24000 \times (1.035)^t[/tex]

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