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Calculus
Your startup company Fabulous Fudge Inc. enters a new market. Your marketing consultants estimate the daily demand for your chocolate bars as
q(p) = 2000; if p < 1;
1000(-p^2 + 2p + 1); if 1 <= p < 2;
1000(p^2 - 6p + 9); if 2 <= p < 3;
0; if 3 <= p:
Here q denotes the quantity demanded per day and p the price per chocolate bar in dollars.
(a) Sketch the graph of demand q(p) as a function of price p.
(b) Compute the price elasticity of demand E(p).
(c) Determine the range of prices p for which demand is elastic, inelastic and unit elastic.
(d) If the price per chocolate bar is 1:2$ and you wish to increase your revenue, should you increase or decrease the unit price?
(e) Determine the price(s) p at which the instantaneous rate of change of revenue with respect to price is zero.
q(p) = 2000; if p < 1;
1000(-p^2 + 2p + 1); if 1 <= p < 2;
1000(p^2 - 6p + 9); if 2 <= p < 3;
0; if 3 <= p:
Here q denotes the quantity demanded per day and p the price per chocolate bar in dollars.
(a) Sketch the graph of demand q(p) as a function of price p.
(b) Compute the price elasticity of demand E(p).
(c) Determine the range of prices p for which demand is elastic, inelastic and unit elastic.
(d) If the price per chocolate bar is 1:2$ and you wish to increase your revenue, should you increase or decrease the unit price?
(e) Determine the price(s) p at which the instantaneous rate of change of revenue with respect to price is zero.
Calculus
You work for Pinstripe Partners LLC, a Cayman Islands based hedge fund founded by one of your fellow students. Your company can both invest and borrow cash at an annual rate of 2% compounded continuously.
(a) You own a derivative contract that will pay out $150 million in 5 years (this
will be the only payment). Your boss instructs you to sell this contract and replace it
with another one which will already pay out in 3 years and which has the same present
value as the existing contract. What will be the sum paid out by the replacement
contract after 3 years?
(b) You have invested $100 million in the company Advantage Electronics Inc.
The value of this investment grows at a rate of 6% per year compounded continuously.
At the same time, you have also invested $80 million in West End Property, growing
at a rate of 8% compounded continuously. After how many years will both investments
have the same value?
(a) You own a derivative contract that will pay out $150 million in 5 years (this
will be the only payment). Your boss instructs you to sell this contract and replace it
with another one which will already pay out in 3 years and which has the same present
value as the existing contract. What will be the sum paid out by the replacement
contract after 3 years?
(b) You have invested $100 million in the company Advantage Electronics Inc.
The value of this investment grows at a rate of 6% per year compounded continuously.
At the same time, you have also invested $80 million in West End Property, growing
at a rate of 8% compounded continuously. After how many years will both investments
have the same value?
Calculus
Compute the first derivative of the following functions.
(a) f(x) = x^x^x
(b) g(x) = (x^x)^x
(c) h(t) = (t^2 + 1)^arctan t
(d) l(y) = ln(y ln y)
(a) f(x) = x^x^x
(b) g(x) = (x^x)^x
(c) h(t) = (t^2 + 1)^arctan t
(d) l(y) = ln(y ln y)
Calculus
You work for the Department of Pathology where you study the growth of a microbial culture of Escherichia coli under very special conditions. The number of bacteria at time t [in hours] can be estimated by
f(t) = (t + 1) e^[√(t+2)]
Use logarithmic differentiation in order to determine the relative growth rate at time t = 3 and give your result in percent growth per hour.
f(t) = (t + 1) e^[√(t+2)]
Use logarithmic differentiation in order to determine the relative growth rate at time t = 3 and give your result in percent growth per hour.
Calculus
The function f(x) = sin(x) with domain D = [-pie/2 ; pie/2 ] is one-to-one. Its inverse function is called f^-1(y) = arcsin(y). (a) Determine the domain and range of arcsin. (b) Calculate the derivative d/dy arctan(y).[Use implicit differentiation]
Calculus
what is the derivative of y=(x)/(x^2+)
Calculus
1.)If y varies directly as x and y=56 when x=8, find y when x=64
2.)Suppose y varies jointly as x and z. Find y when x=18 and z=10,if y=111 when x=4 and z=11
2.)Suppose y varies jointly as x and z. Find y when x=18 and z=10,if y=111 when x=4 and z=11
Calculus
If y varies directly as x and y=15 when x=-5, find y when x=36
Calculus
the ends of a water trough 8 meter long are equilateral triangles whose sides are 2 m long. if the water is being pumped into the trough at a rate of 5 cubic meter per minutes., find the rate at which the water level is rising when the depth is 0.5meter.
Calculus
A= 2X+Y+3Z
B= 3X-2Z
Find a vector C whose magnitude is 6 and whose direction is perpendicular to A and B
B= 3X-2Z
Find a vector C whose magnitude is 6 and whose direction is perpendicular to A and B
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#339914 on Dec 2023
#339914 on Dec 2023