An astronomer observes the velocity of a galaxy at a distance of 100 megaparsecs (Mpc) to calculate its distance two billion years from now using two different models. In the first model, the distance from the galaxy to Earth increases by 9Mpc every billion years. In the second model, the distance from the galaxy to Earth increases by 10 percent every billion years. Two billion years from now, how much further would the galaxy be in the second model compared to the first model in megaparsecs?

Question

An astronomer observes the velocity of a galaxy at a distance of 100 megaparsecs (Mpc) to calculate its distance two billion years from now using two different models. In the first model, the distance from the galaxy to Earth increases by  9Mpc every billion years. In the second model, the distance from the galaxy to Earth increases by 10 percent every billion years. Two billion years from now, how much further would the galaxy be in the second model compared to the first model in megaparsecs?

Bytelearn · Accepted Answer

Calculate Distance Increase: Calculate the distance of the galaxy from Earth in the first model after two billion years. The first model predicts an increase of 9 Mpc every billion years. Therefore, in two billion years, the increase will be 2 times 9 Mpc. Distance increase in the first model = 2 * 9 Mpc = 18 Mpc.Calculate New Distance: Calculate the new distance of the galaxy from Earth in the first model after two billion years. Initial distance = 100 Mpc. Increase in distance = 18 Mpc (from Step 1). New distance in the first model = Initial distance + Increase in distance = 100 Mpc + 18 Mpc = 118 Mpc.Calculate Distance Increase: Calculate the distance of the galaxy from Earth in the second model after one billion years. The second model predicts an increase of 10 percent every billion years. Therefore, after one billion years, the distance will be increased by 10 percent of the initial distance. Distance increase after one billion years in the second model = 10% of 100 Mpc = 0.10 * 100 Mpc = 10 Mpc. New distance after one billion years = Initial distance + Distance increase = 100 Mpc + 10 Mpc = 110 Mpc.Calculate New Distance: Calculate the distance of the galaxy from Earth in the second model after the second billion years. Now, we need to increase the new distance after one billion years by another 10 percent. Distance increase after the second billion years in the second model = 10% of 110 Mpc = 0.10 * 110 Mpc = 11 Mpc. New distance after two billion years = Distance after one billion years + Distance increase after the second billion years = 110 Mpc + 11 Mpc = 121 Mpc.Calculate Difference in Distances: Calculate the difference in distances between the two models after two billion years. Distance in the second model after two billion years = 121 Mpc (from Step 4). Distance in the first model after two billion years = 118 Mpc (from Step 2). Difference in distances = Distance in the second model - Distance in the first model = 121 Mpc - 118 Mpc = 3 Mpc.

Full solution

More problems from GCF and LCM: word problems

Related topics