90. Expanding supernova: The surface area of a star goes through an expansion ph
ID: 2886600 • Letter: 9
Question
90. Expanding supernova: The surface area of a star goes through an expansion phase prior to going supernova. As the star begins expanding, the radius becomes a function of time. Suppose this function is r(t) 1.05t, where t is in days and r(t) is in gigameters (Gm). (a) Find the radius of the star two days after the expansion phase begins. (b) Find the surface area after two days. (c) Express the surface area as a function of time by finding h(t)(Sor)(t), then use h(t) to compute the surface area after two days directly. Do the answers agree? 2Explanation / Answer
r = 1.05t
a)
Two days after :
1.05 *2
2.10
or 2.1 Gm
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b)
SA = 4*pi*r^2
SA = 4*pi*(2.1)^2
SA = 17.64pi square gigameter
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c)
h = (S o r)(t)
h(t) = S(r(t))
= S(1.05t)
But S(r) = 4pi*r^2
So, we have
4pi*(1.05t)^2
SA = 4pi * 1.05^2 * t^2
SA = 4.41pi * t^2 -----> ANS
Now, after 2 days,
4.41pi * 2^2
17.64pi square gigameter ----> ANS
Yes, answers agree!
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