The table lists the distances (in megaparsecs; 1 megaparsec = 3.085 * 1024 cm, and 1 megaparsec = 3.26 million light-years) and velocities (in kilometers per second) of four galaxies moving rapidly away from Earth.

(a) Plot the data using distances for the x-values and velocities for the y-values. What type of relationship seems to hold between the data?

(b) Find a linear equation in the form y = mx that models these data using the points 1520, 40,0002 and 10, 02. Graph the equation with the data on the same coordinate axes.

(c) The galaxy Hydra has a velocity of 60,000 km per sec. How far away, to the nearest megaparsec, is it according to the model in part (b)? 

(d) The value of m is the Hubble constant. The Hubble constant can be used to estimate the age of the universe A (in years) using the formula

Approximate A using the value of m. Round to the nearest hundredth of a billion years.

(e) Astronomers currently place the value of the Hubble constant between 50 and 100. What is the range for the age of the universe A?

Transcribed Image Text:

Velocity Galaxy Distance Virgo 1600 15 Ursa Minor 200 15,000 Corona Borealis 290 24,000 Bootes 520 40,000