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MartinTDL
09.11.2019 •
Mathematics
Over the past several years, the owner of a boutique on aspen avenue has observed a pattern in the amount of revenue for the store. the revenue reaches a maximum of about $ 59000 in april and a minimum of about $ 29000 in october. suppose the months are numbered 1 through 12, and write a function of the form f(x)=asin(b[x−c])+d that models the boutique's revenue during the year, where x corresponds to the month. if needed, you can enter π=3. as 'pi' in your answer.
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Ответ:
Step-by-step explanation:
Given that the revenue reaches a maximum of about $ 59000 in April and a minimum of about $ 29000 in October. Suppose the months are numbered 1 through 12, where the months are numbered 1 through 12
Then minimum when x=10 and maximum when x = 4
Average = 44000 correspond to middle line
Amplitude =![59000-44000 = 15000](/tpl/images/0366/7461/7d04e.png)
Hence the function roughly would be
So we found out two values for A and D
To find values for B and C
The minimum of sine function corresponds to -pi/2 here it is 10 and maximum pi/2 here is 4.
Period = 12 months
So B = coefficient of X =![\frac{12}{2\pi} \\=\frac{6}{\pi}](/tpl/images/0366/7461/1f0c2.png)
Because symmetrical about x=7 we have x-7 with a negative sign since min atx =10
Ответ:
Step-by-step explanation:
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