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user100 [1]
3 years ago
7

Juanita is the self-employed owner of Juanita's Linens. Her estimated annual earnings are $73,040 and she expects to pay 27% of

this amount in income tax. What will be her quarterly estimated tax payment for the third quarter? (For self-employed persons, social security tax is 12.4% of wages up to $106,800, and Medicare tax is 2.9% of all wages.)
Mathematics
1 answer:
adell [148]3 years ago
7 0

Answer:

  $7724

Step-by-step explanation:

Her estimated quarterly income is $73,040/4 = $18,260.

Her estimated tax rate is ...

  27% + 12.4% + 2.9% = 42.3%

This tax rate applied to her estimated earnings gives an estimated quarterly tax of ...

  $18,260 × 0.423 = $7723.98

  ≈ $7724 . . . . . taxes are rounded to the nearest dollar

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Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

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To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

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To find the derivative you need to:

\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t

To find the population growing at the start of 2014 we say t = 0

P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year

To find the population growing at the start of 2015 we say t = 1

P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year

To convert billion to million you multiple by 1000

P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year

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