   Chapter 11.2, Problem 51E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Pollution Pollution levels in Lake Sagamore have been modeled by the equation x = 0.05 + 0.18 e − 0.38 t where x is the volume of pollutants (in cubic kilometers) and t is the time (in years). What is the rate of change of x with respect to time?

To determine

To calculate: The rate of change of x with respect to time if the equation x=0.05+0.18e0.38t represents the pollution level in the Lake Sagamore where x is the volume of pollutants and t is the time (in years).

Explanation

Given Information:

Pollution level in Lake Sagamore is modeled by the equation,

x=0.05+0.18e0.38t

Where, x is the volume of pollutants and t is the time (in years).

Formula used:

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

Calculation:

Consider the provided function,

x=0.05+0.18e0.38t

Where, x is the volume of pollutants and t is the time (in years).

Differentiate both sides with respect to t,

dxdt=ddt(0.05+0.18e0.38t)=ddt(0

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