Mathematics Worksheet Assignment | Get Paper Help

show work completely every step by step asking for question. also box the answer for every questionInstruction: In order to get full credit on each problem, your solution should be clear and well
written with a completed work.
1. Iguanas are cold-blooded organisms with their body temperature depending on the external
temperature. The iguana’s temperature cycles during the day, with a low of 750F at about 3 am (t =
3) and a high of 1040F at about 3 pm at about 3 pm (t = 15). Assume that the body temperature of
an iguana can be modeled by the following function.
T (t ) = A sin(Bt −C )+D
a) Use the data above to find the approximate values for the parameters A, B, C, and D.
b) Sketch a graph of the temperature model T(t) you found in part (a) for one day, 0 ≤t ≤ 24 ,
(Label the x- and y-axis and the name of the graph)
2. For the following DDS: xn +1 = −1.5xn +5
a) Determine whether the DDS is linear or not.
b) Find the equilibrium value(s).
c) Find the explicit solution.
d) Determine the stability of the equilibrium.
3. An operator of a recreational finishing enterprise starts with 4000 catfish in his lake. The number
of catfish increases by 8% per month, and he gives out licenses for a catch of 400 fish per month.
a) Write a recursive model for the number of catfish n months after he starts his business.
b) Find the fish population after 3 months using the recursive equation.
c) Find the explicit solution for the DDS.
d) What is the fish population in the long run? Is this a sustainable business?
e) Determine a catch size that will keep the fish population at its equilibrium value?
4. Consider the discrete logistic growth model given by the equation
pn +1 = 2.7pn −0.001( pn )2
where n is measured in weeks.
a) Assume that p0 = 200 and find the population for the next three weeks, p1, p2, and p3.
b) Determine the growth rate and the carrying capacity for this population.
c) Find all the equilibrium values for this model.
5. A fish population grows according to the Ricker model given by pn +1 = 20pn ⋅e −0.003pn
a) If the initial population is p0 = 200 , find the population for the next three years, p1, p2, and p3. Be
sure to round the populations to the nearest integer in each step.
b) Find the equilibrium values for this model.
6. Three species of bacteria are fed three foods, I, II, and III. A bacterium of the first species consumes
1.3 units each of foods I and II and 2.3 units of food III each day. A bacterium of the second species
consumes 1.1 units of food I, 2.4 units of food II, and 3.7 units of food III each day. A bacterium of
the third species consumes 8.1 units of food I, 2.9 units of food II, and 5.1 units of food III each day.
If 16,000 units of food I, 28,000 units of II, and 44,000 units of food III are supplied each day, how
many of each species can be maintained in this environment?
a) Carefully state the names of the variables and what they denote, and then write the system of
equations for this word problem.
b) Solve the system by using https://www.wolframalpha.com/calculators/system-equationcalculator.
Round each value to the nearest whole number.
7. Sal’s Shoes and Fred’s Footwear both have outlets in California and Arizona. Sal’s sells shoes for
$80, sandals for $40, and boots for $120. Fred’s prices are $60, $30, and $150 for shoes, sandals,
and boots, respectively. Half of all sales in California stores are shoes, ¼ are sandals, and ¼ are
boots. In Arizona the fractions are 1/5 shoes, 1/5 sandals, and 3/5 boots.
a) Write 2 X 3 matrix called P representing prices for the two stores and three types of footwear.
State the meaning of the rows and columns.
b) Write 3 X 2 matrix called F representing the fraction of each type of footwear sold in each state.
State the meaning of the rows and columns.
c) Only one of the two products PF and FP is meaningful. Determine which one it is, calculate the
product, and describe what the entries represent.
d) From your answer to part c, what is the average price for a pair of footwear at an outlet of
Fred’s in Arizona?
8.