math question

Math 112 Applied Calculus II Online Assignment

INSTRUCTIONS:

• Complete the problem given below. Write your solution neatly on blank or lined paper (messy, un-readable work will not be graded).

• Download the free app called Adobe Scan.

• Use the app to scan your completed work, and submit the PDF on C4 by Friday, April 3rd at 11:59PM (note: email submissions and submissions that do not use Adobe Scan will not be graded).

Recall that the average value of a single-variable function f(x) continuous on an interval

[a, b] is given by 1

b − a

∫ b a

f(x)dx.

This is extended to a multi-variable function g(x, y) continuous on a region R by the formula

1

A

∫∫ R

g(x, y)dxdy,

where A is the area of the region R.

Use this formula to answer the following question:

Question 1 AA/6

Suppose that the population of a certain town is modelled by the formula

P(x, t) = 8000e0.5t

1 + x

where x is the distance in kilometres from the city centre, and t is the number of years since January 1, 2010.

Find the average population of this town within 4 km of the city centre, during the period from Jan. 1 2016, to Jan. 1 2019.

1 Math 112B Online Assignment

28-03-2020