Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.12 - Modeling Variation - 1.12 Exercises - Page 129: 49

Answer

a) $16,000,00E_{EARTH}$ b) $193, 067,034,0(E_{EARTH})$

Work Step by Step

a) As per the given problem, we have: $E=kT^4$ Here, $k$ is defined as constant of proportionality $\dfrac{E_{SUN}}{E_{EARTH}}=\dfrac{kT^4_{SUN}}{kT^4_{EARTH}}$ Plug the given data in the above expression, we get This gives: $E_{SUN}=16,000,00E_{EARTH}$ b) As per the given problem, we have: $E'=kAT^4$ Here, $k$ is defined as constant of proportionality $\dfrac{E'_{SUN}}{E_{EARTH}}=\dfrac{kA_{SUN}T^4_{SUN}}{kA_{EARTH}T^4_{EARTH}}$ Plug the given data in the above expression, we get This gives: $E_{SUN}=(\dfrac{6000}{300})^4\dfrac{kA_{SUN}T^4_{SUN}}{kA_{EARTH}T^4_{EARTH}}=193, 067,034,0(E_{EARTH})$
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