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Verizon [17]
3 years ago
9

Find the exponential function passing through points (-1,4/3) and (3,108)

Mathematics
2 answers:
guajiro [1.7K]3 years ago
8 0

Answer:

its 152 i know cause i just did this....

Step-by-step explanation:

Gwar [14]3 years ago
8 0

<u>Answer:</u>

An exponential function is in the general form   \mathrm{y}=\mathrm{a}(\mathrm{b})^{\mathrm{x}}

<u>Explanation:</u>

(x,y) = (-1,4/3) and (x,y)=  (3,108) are the given functions  

Therefore,  

    \frac{4}{3}=a(b)^{-1}=\frac{a}{b}

        \frac{4}{3}=\frac{a}{b}  - eq(1)

           108=a(b)^{3}=a b^{3}=108-e q(2)

Multiply both sides of the first equation by b to find that

       \frac{4}{3} b=a

Substituting in eq-2 we get

      \frac{4}{3} b^{4}=108

    b^{4}=81

  \mathrm{b}=\pm 3

  \mathrm{b}=+3, \text { then } 108=\mathrm{a}(3)^{3}

which gives a = 4,  

henceforth the equation becomes as   \mathrm{y}=4(3)^{\mathrm{x}}

    \mathrm{b}=-3 \text { then } 108=\mathrm{a}(-3)^{3}

which gives a = -4,  

henceforth the equation becomes as y =  -4(-3)^{x}

However! In an exponential function, b>0, otherwise many issues arise when trying to graph the function.

The only valid function is  4(3)^{x}      

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The 5 - number summary of the distribution obtained from the boxplot is :

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Firstly, we need to extract the values for the amount spent by females :

20, 25, 25, 35, 37, 38, 39, 43, 45, 46, 50, 53, 60, 70, 85, 100

The five number summary include ;

  • Minimum, lower Quartile, Median, Upper Quartile and Maximum values.

Rearranging the data in ascending order :

20, 25, 25, 35, 37, 38, 39, 43, 45, 46, 50, 53, 60, 70, 85, 100

The boxplot clearly and easily gives the five number summary of the distribution :

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  • Lower quartile = 35 (starting point of the box)
  • Median = 44 (vertical line in between the box)
  • Upper quartile = 58 (endpoint of the box)
  • Maximum = 85 (endpoint of the upper whisker).

Outlier :

  • Lower boundary = LOWER QUARTILE - (1.5 × IQR)
  • Upper boundary = UPPER QUARTILE + (1.5 × IQR)
  • IQR = UPPER QUARTILE - LOWER QUARTILE
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Lower boundary = 35 - (1.5 × 23) = 0.5

Upper boundary = 58 + (1.5 × 23) = 92.5

  • The point denoted by a dot on the boxplot is an outlier = 100

Hence, values lesser than 0.5 or greater than 92.5 are outliers.

Therefore, 100 is an outlier.

Learn more : brainly.com/question/24582786

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