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Exp. & Log. Functions Assignment
1. Find the derivatives of each of these functions:
a) y = ln?(2x3+7).
b) y= (3x2)/e2x
c) y= 3(4x+3).ln?(4x+3)
d) y= 2x2/(e2x+ x3 )
2. Use the process of implicit differentiation to find dy/(dx) given that x2ey-y2ex = 0.
3. Sketch the graph of the function y = x3ex
4. Use logarithmic differentiation to find the derivative of the function y = ((x+3)4.(2x2+5x)3))/√(4x-3)
5. The percentage of people who have switched to a new social network y years after it was introduced is modelled by the function
p = 100/(1+9e-y)
a) What percentage of the people switched immediately?
b) How long did it take before 75% of the population had switched?
c) After how many years was the new network growing the fastest?
d) Sketch the function.
e) Give a possible explanation for the shape of the curve.
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How could you verify this? Create a null and alternate hypothesis for one of these issues.
The accompanying diagram shows the current macroeconomic situation for the economy of Brittania; real GDP is Y1, and the aggregate price level is P1.
Apply the ERR method with ? = 12% per year to the following series of cash flows. Is there a single, unique IRR for these cash flows?
Comment briefly on the meaning of each of the following Estimated coefficient.
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