   Chapter 2.2, Problem 94E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Climate Change Another greenhouse gas is methane. According to figures from the Intergovernmental Panel on Climate Change (IPCC), the amount of methane in the atmosphere (in parts of volume per billion) can be approximated by C ( t ) ≈ 720 e 0.00351 t parts per billion, where 1 is time in years since 1750.29a. Use the model to estimate the amount of methane in the atmosphere in 1950, 2000, 2050, and 2100. (Round your answers to the nearest 10 parts per billion.)b. According to the model, when, to the nearest decade, will the level surpass 2,000 parts per billion?

(a)

To determine

To calculate: The amount of methane in the atmosphere in 1950, 2000, 2050, and 2100 if According to Intergovernmental Panel on Climate Change (IPCC), the amount of methane in the atmosphere (in parts of volume per million) can be expressed as,

C(t)720e0.00351t parts per billion

Explanation

Given Information:

According to Intergovernmental Panel of Climate Change (IPCC), the amount of methane in the atmosphere (in parts of volume per million) can be expressed as,

C(t)720e0.00351t parts per billion

Here, t is time in year since 1750.

Calculation:

Consider the formula of amount of carbon di oxide,

C(t)720e0.00351t parts per billion

To find the time methane concentration in 1950, first find the value of t.

t=19501750=200

Now substitute t=200 in the expression C(t)720e0.00351t parts per billion.

C(200)720e0.00351(200) parts per billion1450 parts per billion

The methane concentration in 1950 is 1.453×103 parts per billion.

To find the time methane concentration in 2000, first find the value of t.

t=20001750=250

Now substitute t=250 in the expression C(t)720e0.00351t parts per billion.

C(250)720e0.00351(250) parts per billion1730 parts per billion

The methane concentration in 2000 is 1730 parts per billion

(b)

To determine

To calculate: The time when methane level in atmosphere surpasses 2000 parts per billion.

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