Answer:
y = 5·4^x
Step-by-step explanation:
If you have two points, (x1, y1) and (x2, y2), whose relationship can be described by the exponential function ...
y = a·b^x
you can find the values of 'a' and 'b' as follows.
Substitute the given points:
y1 = a·b^(x1)
y2 = a·b^(x1)
Divide the second equation by the first:
y2/y1 = ((ab^(x2))/(ab^(x1)) = b^(x2 -x1)
Take the inverse power (root):
(y2/y1)^(1/(x2 -x1) = b
Use this value of 'b' to find 'a'. Here, we have solved the first equation for 'a'.
a = y1/(b^(x1))
In summary:
- b = (y2/y1)^(1/(x2 -x1))
- a = y1·b^(-x1)
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For the problem at hand, (x1, y1) = (2, 80) and (x2, y2) = (5, 5120).
b = (5120/80)^(1/(5-2)) = ∛64 = 4
a = 80·4^(-2) = 80/16 = 5
The exponential function is ...
y = 5·4^x
The proposal for the price for a number of shirts given by the four companies can be analyzed graphically, given that each price list gives a straight line, and the result presented using a piecewise function approach as follows:
![\begin{cases} & \text{ if } 20 \leq x\leq 40 \ The \ company \ to \ be \ selected \ is \ Easy \ Calculation\\ & \text{ if } 40 < x \leq 80\ The \ company \ to \ be \ selected \ is \ Shirtee \\ & \text{ if } 80 < x \leq 200\The \ company \ to \ be \ selected \ is \ T-Shirts\ R\ Us \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%20%26%20%5Ctext%7B%20if%20%7D%2020%20%5Cleq%20%20x%5Cleq%2040%20%5C%20The%20%5C%20company%20%5C%20to%20%5C%20be%20%5C%20selected%20%5C%20is%20%5C%20Easy%20%5C%20Calculation%5C%5C%20%26%20%5Ctext%7B%20if%20%7D%2040%20%3C%20x%20%5Cleq%2080%5C%20The%20%5C%20company%20%5C%20to%20%5C%20be%20%5C%20selected%20%5C%20is%20%5C%20Shirtee%20%5C%5C%20%26%20%5Ctext%7B%20if%20%7D%2080%20%3C%20x%20%5Cleq%20200%5CThe%20%5C%20company%20%5C%20to%20%5C%20be%20%5C%20selected%20%5C%20is%20%5C%20T-Shirts%5C%20R%5C%20Us%20%5Cend%7Bcases%7D)
<h3>What is a piecewise function?</h3>
A piecewise defined function is one that has other sub functions which are applied over different intervals of the domain.
The given table of values and equation are plotted on a graph using MS Excel
From the graph, and the table created, we have:
When the number of shirts on order is less than 40, the least expensive is Easy Calculation shirts
When the number of shirts are more than 40 but less than 80, the least expensive proposal is given by Shirtee
When the number of shirts to be ordered is more than 80, the company that gives the least expensive proposal is T-Shirts R Us
The selection table is presented as follows:
![\begin{cases} & \text{ if } 20 \leq x\leq 40 \ The \ company \ to \ be \ selected \ is \ Easy \ Calculation\\ & \text{ if } 40 < x \leq 80\ The \ company \ to \ be \ selected \ is \ Shirtee \\ & \text{ if } 80 < x \leq 200\The \ company \ to \ be \ selected \ is \ T-Shirts\ R\ Us \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%20%26%20%5Ctext%7B%20if%20%7D%2020%20%5Cleq%20%20x%5Cleq%2040%20%5C%20The%20%5C%20company%20%5C%20to%20%5C%20be%20%5C%20selected%20%5C%20is%20%5C%20Easy%20%5C%20Calculation%5C%5C%20%26%20%5Ctext%7B%20if%20%7D%2040%20%3C%20x%20%5Cleq%2080%5C%20The%20%5C%20company%20%5C%20to%20%5C%20be%20%5C%20selected%20%5C%20is%20%5C%20Shirtee%20%5C%5C%20%26%20%5Ctext%7B%20if%20%7D%2080%20%3C%20x%20%5Cleq%20200%5CThe%20%5C%20company%20%5C%20to%20%5C%20be%20%5C%20selected%20%5C%20is%20%5C%20T-Shirts%5C%20R%5C%20Us%20%5Cend%7Bcases%7D)
Learn more about piecewise defined functions here:
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Answer: 8
Step-by-step explanation: if you count the angels and the sides then you'll get the answer 8..
9514 1404 393
Answer:
The given graph shows a function of x.
Step-by-step explanation:
Neither 1 nor 3 is a single-valued relation for some values of x. The graph shown passes the vertical line test, so does represent a function.
The graph is a relation that is a function of x.
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The attached graph is of the equation of 3. A vertical line will intersect the graph in more than one place, so the relation is NOT a function.
Answer:
62
Step-by-step explanation:
this is because 62 might be 100%