Answer
(a) See graph, linear.
(b) $y=77x$, see graph.
(c) $779$ megaparsec.
(d) $12.34\ billion$ years.
(e) from 9.5 to 19 billion years.
Work Step by Step
(a) See graph, the relationship appears to be linear.
(b) Use points $(520,40000)$ and $(0,0)$, we have $m=\frac{40000}{520}\approx77$ and $y=77x$, see graph.
(c) For $y=60000$, we have $x=60000/77\approx779$ megaparsec.
(d) With $m=77$, use the formula, we have $A=\frac{9.5\times10^{11}}{77}\approx12.34\ billion$ years.
(e) For $m_1=50$, we have $A_1=\frac{9.5\times10^{11}}{50}=19\ billion$ years. For $m_2=100$, we have $A_2=\frac{9.5\times10^{11}}{100}=9.5\ billion$ years. Thus the range is from 9.5 to 19 billion years.
