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2 years ago

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Danielle is a realtor. She receives a salary of $500 per month plus a 6% commission on each house the she sells. Which represent

ation shows the relationship between x, Danielle's total sales for the month, and y, her monthly income

1 answer:

OverLord2011 [107]2 years ago

8 0

Answer:

The relationship between x, Danielle's total sales for the month, and y, her monthly income is as shown;

y=0.06 x+500

Step-by-step explanation:

Step 1: Express the monthly income

The monthly income can be expressed as follows;

y=F+(R×x)

where;

y=her monthly income

F=fixed income per month

R=commission rate

x=total number of houses she sells

In our case;

Monthly income=y

F=$500 a month

R=6%=6/100=0.06

total number of houses she sell=x

replacing;

y=500+(6% of x)

y=500+(0.06×x)

y=500+0.06 x

The relationship between x, Danielle's total sales for the month, and y, her monthly income is as shown;

y=0.06 x+500

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(a) Suppose $h_n=r^n$ is a solution for this recurrence, with $r\neq0$ . Then

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So we expect a general solution of the form

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With $h_0=0,h_1=1,h_2=1,h_3=2$ , we get four equations in four unknowns:

$\begin{cases}c_1+c_2=0\\-c_1+2c_2+2c_3+2c_4=1\\c_1+4c_2+8c_3+16c_4=1\\-c_1+8c_2+24c_3+72c_4=2\end{cases}\implies c_1=-\dfrac8{27},c_2=\dfrac8{27},c_3=\dfrac7{72},c_4=-\dfrac1{24}$

So the particular solution to the recurrence is

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