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alexciamartinez05
12.06.2020 •
Mathematics
The following data values represent the selling prices of houses in a neighborhood. Which measure of central tendency is most appropriate for describing this data? $90000, $100000, $97000, $93000, $89000, $103000, $95000, $85000, $91000, $350000, $96000, $91000
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Ответ:
9.1%
Step-by-step explanation:
Use the compound amount formula:
A = P(1 + r/n)^(nt), where P is the principal ($5000), r is the interest rate as a decimal fraction and is to be determined; n is the number of compounding periods per year (1 in this case), and t is the number of years.
Here we have A = double P = 2P =P(1+r/1)^(1*8), or
2 = (1+r)^8
We solve this for r by taking the natural logarithm of both sides:
ln 2 = 8*ln(1+r), or (after dividing both sides by 8)
ln 2
= ln (1+r)
8
0.6931
Since ln 2 = 0.6931, we have = 0.0866 = ln (1+r)
8
Raise the base e to the power 0.0866 on the left side and raise the base e to the power ln (1+r) on the right side, obtaining:
1.091 = 1 + r
Subtracting 1 from both sides yields the desired value of r:
0.091 = r
The interest rate must be 9.1% for Jon's $5000 to double in eight years.