In January 2011 the rate of VAT increased from 17.5% to 20%

Mathematics

1 answer:

Sergio [31]2 years ago

7 0

Answer:

Difference between in price of a car due to increase in VAT is $375.

Step-by-step explanation:

Since e have given that

Price of car = $15000

Rate of VAT = 17.5%

So, Amount of tax becomes

So, Total Price he has to pay is given by

but According to question,

Rate of VAT = 20%

So, Amount of tax becomes

So, Total price he has to pay is given by

Difference between both the price due to increase in VAT is given by

Hence, difference between in price of a car due to increase in VAT is $375.

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Answer:

The answer is shown below

Step-by-step explanation:

Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.

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$\frac{dy}{dt}=ky(1-y)\\\frac{dy}{y(1-y)}=kdt\\\int\limits {\frac{dy}{y(1-y)}} \, =\int\limit {kdt}\\\int\limits {\frac{dy}{y}} +\int\limits {\frac{dy}{1-y}} =\int\limit {kdt}\\\\ln(y)-ln(1-y)=kt+c\\ln(\frac{y}{1-y}) =kt+c\\taking \ exponential \ of\ both \ sides\\\frac{y}{1-y} =e^{kt+c}\\\frac{y}{1-y} =e^{kt}e^c\\let\ A=e^c\\\frac{y}{1-y} =Ae^{kt}\\y=(1-y)Ae^{kt}\\y=\frac{Ae^{kt}}{1+Ae^{kt}} \\at \ t=0,y=10\%\\0.1=\frac{Ae^{k*0}}{1+Ae^{k*0}} \\0.1=\frac{A}{1+A} \\A=\frac{1}{9} \\$