Modeling Luxury Home Sales The following quadratic function in general form,

melodykap

melodykap

Answered question

2021-09-15

Modeling Luxury Home Sales
The following quadratic function in general form, S(t)=5.8t281.2t+1200 models the number of luxury home sales, S(t), in a major Canadian urban area, according to statistical data gathered over a 12 year period. Luxury home sales are defined in this market as sales of properties worth over $3 Million (inflation adjusted). In this case, t=0 represents 2000 and t=11 represents 2011. Use a calculator to find the year when the smallest number of luxury home sales occurred. Without sketching the function, interpret the meaning of this function, on the given practical domain, in one well-expressed sentence.

Answer & Explanation

Elberte

Elberte

Skilled2021-09-16Added 95 answers

Step 1
Given:
The number of luxury home sales S(t) in a major Canadian urban arca over a period of 12 year is given by:
S(t)=5.8t281.2t+1200
Step 2
For minimum number of sales:
dS(t)dt=0
d(5.8t281.2t+1200)dt=0
11.6t81.2=0
11.6t=81.2
t=81.211.6
t=7
Step 3
So, minimum number of sales is given by
S(7)=5.8(7)281.2(7)81.2(7)+1200
S(7)=284.2568.4+1200
S(7)=915.8
S(7)=916

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