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Unit 3 – Radicals and Rational Exponents

March 24, 2016 | Author: | Posted in mathematics, mathematics and economics

Unit 3 – Radicals and Rational Exponents

Line

Fahrenheit temperature F is a linear function of Celsius temperature C This function is following . Hence , ignites at 233 ?C

Parabola

The amount of nitrogen dioxide (NO2 ) present in the air in the city of Springfield on a certain day in July (2006 ) is shown in the accompanying figure , presented below

The equation for this graph is A (t -2t2 32t 42 , where t ‘ is the number of hours after 6 :00 a .m . Using this function it is easy to find the [banner_entry_middle]

moment when the level of NO2 will be maximum on that day . The maximum value was fixed at 8 hours after 6 :00 a .m (namely at 2 :00

.m (tmax -b (2a -32 (2 (-2 32 /4 8 . The level of nitrogen dioxide at this time is 170 parts per million (A (8 -2 82 32 8 42 170

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Hyperbola

The case for application of hyperbola in real life can be described by the following example . Every year a farmer plants potato on a field of certain area . However , there is a building site not far from his field and with each year it expands more and more . So each year the farmer is forced to narrow his d . How much must be the field lengthened to keep the same is the area of the field , y is the length of the field , x is the width of the field . Then

and

The graph of this function is hyperbola . This particular graph is very simple , and everyone can simply imagine it

Exponential

The exponential function describes the population growth . The formula for population growth is 2

f

v

r

t

yu

h[

people in 1964 , then we can derive the P0 and k in function

(t . P0 2 .75 109 . t is a number of years , that had passed since 1964 . 1994 – 1964 30 , then

P (30 5 .5 109

P (30 2 .75 109 e30k

5 .5 109 2 .75 109 e30k

2 e30k

k 0

Hence , the world population growth describes by the following formula Now it can be easy derived the year , when the world population will become 10 109 people

P (t 10 109

10 109 2 .75 109 e0 .0231t

10 2 .75 e0 .0231t

e0 .0231t 3 .6364

t ? 56 years (after 1964

Hence , the world population will become 10 109 people in 2020 year… [banner_entry_footer]

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