MATH 1210 Week 2 Assignment

MATH 1210 Week 2 Assignment | Tulane University

Module 2Quiz

Solve the problems below and write up a solution to each problem using complete English sentences and well-organized calculations as appropriate. Your solution will be graded based on mathematical accuracy and clarity of presentation.

Late submissions will not be accepted. You must submit your responses as a single .pdf file that includes all pages of your solution. You may resubmit until the deadline but only the most recent submission will be graded. Quiz submissions will not be accepted via e-mail. After submitting you must download your file to ensure that it submitted properly. See technical instructions on Module Quiz submissions.

Problem 1

The population of a specific type of organism in a limited environment with initial population 2,000 and is P(t)=200,00020+80e−tP(t)=200,00020+80e−tPP ( t ) = 200 , 000 20 + 80 e − t, where tttt is measured in minutes.

a.    Find the inverse of this function and explain what it means.

b.    Use the inverse function to find the time required for the population to reach 8,000.

Problem 2

According to Boyle’s Law, if the temperature of a confined gas is held fixed, then the product of the pressure PPPP and the volume VVVV is a constant. Assume we are working with a certain gas with PV=500PV=500PP V = 500, where PPPP is measured in pounds per square inch and VVVV is measured in cubic inches.

a.    Can PPPP and VVVV be written as functions in terms of the other variable? Explain.

b.    Find the average rate of change of VVVV as PPPP changes from 100 to 500 pounds per square inch.