# Maths -in a certain country, the percentage of the population

In a certain country, the percentage of the population relocating from one town to another town in that same country is given by the following function:

( )

Time is zero (t = 0) corresponds to the year 1960. The population of the entire country should be considered a constant.

1. Find the rate at which people relocated during the year of your birth. (If you were born before 1960, please use 1960 as your birth-year)

2. Find the relocation rate of today.

What does this tell you about the country’s population? Is there a peak (max) relocation year? Do you think this model is appropriate for predicting population movement? Why or why not?

1. Find the derivative for the following:

a. y = x^2e^x

b. y = (e^x + 2)^3/2

c. Y = e^-3x

d. y = e^-e ^-x/2

2. The present value of a building in the downtown area is given by the function P(t) = 300,00e^-0.09t+vt/2 f or 0< t < 10

Find the optimal present value of the building. (Hint: Use a graphing utility to graph the function, P(t), and find the value of t0 that gives a point on the graph, (t0, P(t0)), where the slope of the tangent line is 0.)

3. Find the equation of the line tangent to f(x) = xe^-x,

at the point where x= 0. What does this tell you about the behavior of the graph when x = 0?

4. The unit selling price p (in dollars) and the quantity demanded x (in pairs) of a certain brand of women’s shoes are given by the demand equation P(x) = 100e^-0.0001x f or 0 < x < 20,000

a. Find the revenue function, R. (Hint: R(x) = x(p(x)), since the revenue function is the unit selling price at a demand level of x units times the number of units demanded.)

b. Find the marginal revenue function, R’

c. What is the marginal revenue when, x = 10?

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