(08.01 LC)

22. An employee joined a company in 2017 with a starting salary of $50,000. Every year this employee receives a raise of $1000 p

Setler79 [48]

Answer:

(a) The recurrence relation for the salary is

$S_{n+1}=1.05*S_n+1000\\\\S_0=50000$

(b) The salary 25 years after 2017 will be $217044.85.

(c) $S_n=1.05^nS_0+1000*\sum_{0}^{n-1}1.05^n$

Step-by-step explanation:

We can define the next year salary $S_{n+1}$ as

$S_{n+1}=S_n+1000+0.05*S_n=1.05*S_n+1000$

wit S0=$50000

If we extend this to 2 years from 2017 (n+2), we have

$S_{n+2}=1.05*S_{n+1}+1000=1.05*(1.05*S_n+1000)+1000\\S_{n+2} =1.05^2*S_n+1.05*1000+1000\\S_{n+2}=1.05^2*S_n+1000*(1.05^1+1)$

Extending to 3 years (n+3)

$S_{n+3}=1.05*S_{n+2}+1000=1.05(1.05^2*S_n+1000*(1.05^1+1))+1000\\\\S_{n+3}=1.05^3S_n+1.05*1000*(1.05^1+1)+1000\\\\S_{n+3}=1.05^3*S_n+1000*(1.05^2+1.05^1+1)$

Extending to 4 years (n+4)

$S_{n+4}=1.05*S_{n+3}+1000=1.05*(1.05^3*S_n+1000*(1.05^2+1.05^1+1))+1000\\\\S_{n+4}=1.05^4S_n+1.05*1000*(1.05^2+1.05^1+1))+1000\\\\S_{n+4}=1.05^4S_n+1000*(1.05^3+1.05^2+1.05^1+1.05^0)$

We can now express a general equation for S_n (salary at n years from 2017)

$S_n=1.05^nS_0+1000*\sum_{0}^{n-1}1.05^n$

The salary at 25 years from 2017 (n=25) will be

$S_{25}=1.05^{25}S_0+1000*\sum_{0}^{24}1.05^i\\\\S_{25}=3.386*50000+1000*47.72=217044.85$

8 0

4 years ago

A bag contains 42 red, 45

AlexFokin [52]

Answer:

31

Step-by-step explanation:

First of,

or, in probability is subtraction and not means you shouldn't use green (therefore leaving you with yellow and red)

Red = 42

Yellow = 20

P(Yellow or Not Green) = $\frac{R+Y}{2}$

⁘ $\frac{42+20}{2}$ = $\frac{62}{2}$

Hence, 31

7 0

2 years ago

How do you calculate the x-intercept of a line written in Standard Form?

serious [3.7K]

To calculate the x-intercept of a line written in standard form you simply remove the "y" and solve for x. And you remove the "x" when solving for y.

y=0 , solve for x
x=0 , solve for y

Here is an example: (solving for x)

2x + 3y = 6
2x + 3(0) = 6
2x = 6
2x/2 = 6/2
x = 3

Here is an example: (solving for y)

2x + 3y = 6
2(0) + 3y = 6
3y = 6
3y/3 = 6/3
y = 2

7 0

4 years ago

Evaluate the function for f(x) = x + 3 and g(x) = x2 − 2. (f − g)(0) (f − g)(0) =

adelina 88 [10]

Hello,

(f-g)(0)=f(0)-g(0)=3-(-2)=5

8 0

3 years ago

3y + 2 = -6x in slope-intercept form : y=mx+b oh and please show work! Thank youuu

Alex

The answer is y = -2/3x -2

Just have to Subtract two on both sides the. Divide all numbers by 3

Could you please mark me brainleist

5 0

3 years ago

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