Posted: August 4th, 2022

# Maths -In a certain country, the percentage of the population relocating

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

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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