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FPMT0107_Fall24

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A survey was conducted to find out the monthly expenditure on groceries of 30 households. 

The data (in rials) are as follows:

bold 220 bold comma bold space bold space bold 340 bold comma bold space bold space bold 290 bold comma bold space bold space bold 200 bold comma bold space bold space bold 310 bold comma bold space bold space bold 260 bold comma bold space bold space bold 300 bold comma bold space bold space bold 340 bold comma bold space bold space bold 360 bold comma bold space bold space bold 280 bold comma bold 330 bold comma bold space bold space bold 310 bold comma bold space bold space bold 250 bold comma bold space bold space bold 270 bold comma bold space bold space bold 290 bold comma bold space bold space bold 320 bold comma bold space bold space bold 350 bold comma bold space bold space bold 340 bold comma bold space bold space bold 300 bold comma bold space bold space bold 390 bold.

(a)   Organize the data into a frequency distribution table with class intervals of width 50 rials.

(b)   Draw a histogram of the data.

(c)   Compute the mean monthly expenditure on groceries.

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Find the time required for an investment of 4000 rials to grow to 5000 rials 

at an interest rate of 7.5 % per year, compounded quarterly.

Round your answer to the nearest year.

Error converting from MathML to accessible text.

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begin mathsize 16px style bold italic P bold italic a bold italic r bold italic t bold space bold italic I bold italic I space space bold italic S bold italic H bold italic O bold italic W bold thin space bold space bold italic A bold italic L bold italic L bold space bold thin space bold italic S bold italic T bold italic E bold italic P bold italic S space space o f space y o u r space w o r k. end style

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Consider the functions  f left parenthesis x right parenthesis equals fraction numerator 5 x minus 3 over denominator 2 x plus 7 end fraction  and  g left parenthesis x right parenthesis equals x minus 1.

(a)   Find the function Error converting from MathML to accessible text..

(b)  The domain of  Error converting from MathML to accessible text. is ...  begin bold style stretchy left parenthesis C h o o s e space t h e space a n s w e r space b e l o w. stretchy right parenthesis end style

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S o l v e space t h e s e space q u e s t i o n s space o n space A 4 space p a p e r comma space bold italic S bold italic H bold italic O bold italic W bold thin space bold thin space bold italic A bold italic L bold italic L bold thin space bold italic S bold italic T bold italic E bold italic P bold italic S space o f space y o u r space w o r k. T a k e space p h o t o s space o f space y o u r space s o l u t i o n s space a n d space u p l o a d space t h e m space i n space bold italic F bold italic i bold italic n bold italic a bold italic l bold space bold italic e bold italic x bold italic a bold italic m bold comma bold space bold space bold italic P bold italic a bold italic r bold italic t bold space bold italic I bold italic I.

Error converting from MathML to accessible text.

(a)   Consider the exponential function  Error converting from MathML to accessible text..

        Use graph transformations to sketch the graph of f.                               

(b)    Solve the exponential equation:   Error converting from MathML to accessible text..                               

        T y p e space t h e space v a l u e space o f bold space bold italic x space i n space t h e space b o x space b e l o w comma space space bottom enclose t h e space n u m b e r space o n l y end enclose.

 

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bold italic P bold italic a bold italic r bold italic t bold space bold italic I bold italic I bold italic S bold italic H bold italic O bold italic W bold thin space bold thin space bold space bold italic A bold italic L bold italic L bold thin space bold space bold italic S bold italic T bold italic E bold italic P bold italic S space space o f space y o u r space w o r k.

 begin mathsize 16px style begin bold style stretchy left square bracket 5 space m a r k s stretchy right square bracket end style end style

Solve the logarithmic equation:   log subscript space 2 space end subscript open parentheses x space minus space 3 close parentheses space equals space 5 space minus space log subscript space 2 space end subscript open parentheses x space plus space 1 close parentheses

 

T y p e space t h e space v a l u e space o f bold space bold italic x space i n space t h e space b o x space b e l o w comma space space bottom enclose t h e space n u m b e r space o n l y end enclose. I f space t h e r e space a r e space t w o space s o l u t i o n s comma space space t y p e colon space space text bold solution1,solution2 end text

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begin mathsize 16px style bold italic P bold italic a bold italic r bold italic t bold space bold italic I bold italic I space space bold italic S bold italic H bold italic O bold italic W bold thin space bold space bold italic A bold italic L bold italic L bold space bold thin space bold italic S bold italic T bold italic E bold italic P bold italic S space space o f space y o u r space w o r k. end style

left square bracket bold 7 bold space text bold marks end text right square bracket

Consider the quadratic function  f left parenthesis x right parenthesis equals 2 x squared space plus space 8 x space plus 7.

(a)   Find the vertex, x- and y-intercepts of f.

(b)   Sketch the graph of f.  

(c)   What is the minimum value of f?

T y p e space y o u r space a n s w e r space f o r space p a r t space left parenthesis bold italic c right parenthesis space i n space t h e space b o x space b e l o w comma space bottom enclose t h e space n u m b e r space o n l y end enclose.

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Find an effective rate equivalent to a nominal rate of 7 1 half percent sign compounding quarterly.

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If a principal of  8000 Rials is invested at an interest rate of 3 space% compounded monthly, find the compound amount after 4 years.

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The population of a city is growing at a rate of 4.5 % per year according to the formula  

                                                  P equals 53 comma 500 space open parentheses 1.045 close parentheses to the power of space t end exponent ,

where t  is the number of years after 2018.   Estimate the population in 2027. 

 

T y p e space y o u r space a n s w e r space i n space t h e space b o x space b e l o w comma space bottom enclose t h e space n u m b e r space o n l y end enclose.

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A trust fund for a child is being set up by a single payment so that after 16 years the child will receive $45000. How much should be paid into the fund if the fund earns an interest rate of 6% compounded semiannually?

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