The number of new songs that a rock group needs to stay at the top each year is inversely proportional to the year and that the group has been in the industry. a. Write an equation of variation. b. If after 3 years in the industry the group needs 50 new songs, how many songs will you need after 5 years?

Answer:  a) [tex]3\times50=5 \times x[/tex]b) 30Step-by-step explanation:Given: The number of new songs that a rock group needs to stay at the top each year is inversely proportional to the year and that the group has been in the industry.Let x be the number of songs will be needed after 5 years.Now the inverse variation equation for the given question will be:-[tex]3\times50=5 \times x\\\\\Rightarrow x=\dfrac{3\times50}{5}\\\\\Rightarrow\ x=30[/tex]Hence , the number songs will be needed after 5 years = 30