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Xia is charging her laptop. She records ...


Xia is charging her laptop. She records the battery charge for the first 30 minutes after she plugs it in to get an idea of when it will be completely charged. The table above shows the results. If y is the percent battery charge on Xia's laptop, which linear equation represents the correct relationship between y and x ?

A

`y = 1.5 x +19`

B

`y =2x+14`

C

`y =2.5x +9`

D

`y =10 x + 34`

Text Solution

Verified by Experts

The correct Answer is:
A
The equatin tells you that the relationship is linear, so start by finding the rate of change (the slop, m) using any two pairs of values from the table and the slope formula. Next substitute the slope and any pair of values from the talbe , such as `(10, 34),` into the equation `y = mx + b` and solve for b. Finally, use the values of m ans b to write the function.
`m = (y _(2) -y_(1))/(x _(2) -x_(1))=(64-34)/(30-10)=1.5`
You can stop right there! Only (A) has a slope of `1.5,` so it mus be the correct answer. For the record :
`34=10(1.5)+b`
`34=15+b`
` 19=b`
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When an atom or an ion is missing from its normal lattice site, a lattice vacancy (Schottky defect) is created. In stoichimetric ionic crystals, a vacancy of one ion has to be accompanied by the vacancy of the oppositely charged ion in order to maintain electrical neutrality. In a Frenkel defect an ion leaves its position in the lattice and occupies an interstitial void. This is the Frenkel defect commonly found along with the Schottky defects and interstitials. In pure alkali halides, Frenkel defects are not found since the ions cannot get into the interstitial sites. Frenkel defects are found in silver halides because of the small size of the Ag^(+) ion. Unlike Schottky defects, Frenkel defects do not change the denstiy of the solids. In certain ionic solids (e.q. AgBr) both Schottky and Frenkel defects occur. The defects discussed above do not disturb the stoichiometry of the crystalline material. There is large variety of non-stoichiomertic inorganic solids which contain an excess or deficiency of one of the elements. Such solids showing deviations from the ideal stoichiometric composition from an inmportant group of solids. For example in the vanadium oxide, VO_(x) , x can be anywhere between 0.6 and 1.3. There are solids which are difficult to prepare in the stoichiometric composition. Thus, the ideal composition in compounds such as FeO is difficult to obtain (normally we get a composition of Fe_(0.95)O but it may range from Fe_(0.93)O " to " Fe_(0.96)O ). Non-stoichiometric behaviour is most commonly found for transition metal compounds though is also known for some lanthanoids and actinoids. Zinc oxide loses oxygen reversibly at high temperature and turns yellow in colour. The excess metal is accommodated interstitially, giving rise to electrons trapped in the neighbourhood. The enhanced electrical conductivity of the non-stoichiometric ZnO arises from these electrons.ltrbgt Anion vacancies in alkali halides are produced by heating the alkali halide crystals in an atmosphere of the alkali metal vapur. When the metal atoms deposit on the surface they diffuse into the crystal and after ionisation the alkali metal ion occupies cationic vacancy whereas electron occupies anionic vacancy. Electrons trapped in anion vacancies are referred to as F-centers (from Farbe the German word for colour) that given rise to interesting colour in alkali halides. Thus, the excess of potassium in KCl makes the crytal appear violet and the excess of lithium in LiCl makes it pink. When LiCl is heated into the vapour of lithium, the crystal acquires pink colour. This is due to

When an atom or an ion is missing from its normal lattice site, a lattice vacancy (Schottky defect) is created. In stoichimetric ionic crystals, a vacancy of one ion has to be accompanied by the vacancy of the oppositely charged ion in order to maintain electrical neutrality. In a Frenkel defect an ion leaves its position in the lattice and occupies an interstitial void. This is the Frenkel defect commonly found along with the Schottky defects and interstitials. In pure alkali halides, Frenkel defects are not found since the ions cannot get into the interstitial sites. Frenkel defects are found in silver halides because of the small size of the Ag^(+) ion. Unlike Schottky defects, Frenkel defects do not change the denstiy of the solids. In certain ionic solids (e.q. AgBr) both Schottky and Frenkel defects occur. The defects discussed above do not disturb the stoichiometry of the crystalline material. There is large variety of non-stoichiomertic inorganic solids which contain an excess or deficiency of one of the elements. Such solids showing deviations from the ideal stoichiometric composition from an inmportant group of solids. For example in the vanadium oxide, VO_(x) , x can be anywhere between 0.6 and 1.3. There are solids which are difficult to prepare in the stoichiometric composition. Thus, the ideal composition in compounds such as FeO is difficult to obtain (normally we get a composition of Fe_(0.95)O but it may range from Fe_(0.93)O " to " Fe_(0.96)O ). Non-stoichiometric behaviour is most commonly found for transition metal compounds though is also known for some lanthanoids and actinoids. Zinc oxide loses oxygen reversibly at high temperature and turns yellow in colour. The excess metal is accommodated interstitially, giving rise to electrons trapped in the neighbourhood. The enhanced electrical conductivity of the non-stoichiometric ZnO arises from these electrons.ltrbgt Anion vacancies in alkali halides are produced by heating the alkali halide crystals in an atmosphere of the alkali metal vapur. When the metal atoms deposit on the surface they diffuse into the crystal and after ionisation the alkali metal ion occupies cationic vacancy whereas electron occupies anionic vacancy. Electrons trapped in anion vacancies are referred to as F-centers (from Farbe the German word for colour) that given rise to interesting colour in alkali halides. Thus, the excess of potassium in KCl makes the crytal appear violet and the excess of lithium in LiCl makes it pink. Stongly heated ZnO crystal can conduct electricity. This is due to

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