1.) An online company sells handmade samurai katana swords. The website costs $1

Question

1.) An online company sells handmade samurai katana swords. The website costs $190 a month to maintain. Each katana costs $265 to make, and they sell each katana for $760.

b.) Using this model, find the number of swords that would need to be sold per month to have a monthly profit of $ 3660: ________________

2.) The population of the world in 1990 was 45 billion and the relative growth rate was estimated at 0.45 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2018. Your answer is ________________ billion.

3.) A particular type of bacteria grows at a rate of 17% per day. If my hyena got infected with 700 bacterium when his leg was cut by barbed wire, how many bacterium will be present in 3 days when I finally decide I need to take the hyena to the veterinarian? Answer: _____________ bacterium

Explanation / Answer

a. Sale price of each katana = $760

Cost of making each katana=$265.

Contribution from each katana sold= 760-265= $495

Assume the fixed cost is $190=y0 a month ,and x units sold a month,

Profit =y

So, Profit = no of units sold*495- 190

Or, y=x*495-190

Or y=495x-y

Therefore the linear equation is y=495x-190

b. for y =3660 , the equation will be ,

3660=495x-190

Or, x= 7.78 or 8 approx.

Therefore 7.78 or 8 katanas to be sold each month to have $3660 profit per month.

Exponential equation;

Y(t) = a *ekt

Where y (t) = no at time t

A = initial no= 45 billion

K=growth rate=0.45% a year

T=time=28 years

So, Y (2018) = 45*e0.0045*28=45*e0.126=45*1.134= 51.03

So the population in 2018 will be 51.03 billion.

Bacteria after 3 days will be y(3)= 700*e0.17*3=700*e0.51=700*1.665=1165.50

Therfore the bacteria count in hyena after 3 days will be = 1166

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