   Chapter 12, Problem 37RE ### 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

# Oxygen levels in water The rate of change of the oxygen level (in mmol/1) per month in a body of water after an oil spill is given by P ' ( t ) = 400 [ 5 ( t + 5 ) 2 − 50 ( t + 5 ) 3 ] where t is the number of months after the spill. What function gives the oxygen level P at any time t if P = 400 mmol/1 when t = 0?

To determine

To calculate: The function that give the oxygen level P at any time t if P=400mmol/1 when t=0 where the rate of change of the oxygen level (in mmol/l) per month in a body of water after an oil spill is P(t)=400[5(t+5)250(t+5)3] and t is the number of months after the spill.

Explanation

Given information:

It is provided that the rate of change of the oxygen level is P(t)=400[5(t+5)250(t+5)3].

Formula used:

The oxygen level P at any time t is given by the integral of the rate of change of the oxygen level (in mmol/l) per month in a body of water as,

P(t)=Pdt

Calculation:

Consider the provided equation,

P(t)=400[5(t+5)250(t+5)3]

Use the formula of production to calculate the number of units produced as,

P(t)=(400[5(t+5)250(t+5)3])dt=(400[5(t+5)2])dt+(400[50(t+5)3])dt+C=400[5(t+5)1(1)50(t+

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