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3 years ago

11. A company plans to have coffee mugs produced with the company logo on them. The cost of each

Mathematics

1 answer:

vovikov84 [41]3 years ago

6 0

Answer:

Step-by-step explanation:

The cost of each mug depends on the number of mugs that are ordered and is modeled by :

$y =0.0001x^2+ 0.1x + 30$ ...(1)

We need to find the minimum cost of each mug.

For minimum cost, dy/dx = 0

So,

$\dfrac{d(0.0001x^2- 0.1x + 30)}{dx}=0\\\\2x(0.0001)-0.1=0\\\\0.0002x=0.1\\\\x=\dfrac{0.1}{0.0002}\\\\x=500$

Put the value of x in equation (1).

$y =0.0001(500)^2- 0.1(500) + 30\\\\y=5$

So, the minimum cost of each mug is $5.

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A. The city we will use is Orlando, Florida, and we are going to examine its population growth from 2000 to 2010. According to the census the population of Orlando was 192,157 in 2000 and 238,300 in 2010. To examine this population growth period, we will use the standard population growth equation $N_{t} =N _{0}e^{rt}$
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We just show that Orlando's population has been growing at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

B. Here we will examine the population decline of Detroit, Michigan over a period of ten years: 2000 to 2010.
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Population in 2010: 713,777
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