Question

There are 15 people in the course. Each year the number of people in the chorus increases by 3. There are 30 people in the band. Each year 2 new people join the band. Part A: write a function to represent the number of people in the chorus throughout the years. Part B: write a function to represent the number of people in the band throughout the years.Part C: how many people are the chorus after 9 years? How many people are in the band after the same amount of years?Part D: approximately how many years has the number of people in the chorus and the number of people in the band the same? Justify your answer mathematically.

Answer 1

A.

There are 15 people in the chorus and each year the pepople increases by 3. Let t represent the number of years. Then each year the number of people is:

`f(t)=3t+15`

B.

There are 30 people in the band, each year the people increases by 2. Let t represent the number of years. Then each year the numbe of people in the band is:

`g(t)=2t+30`

C.

After 9 years the number of people will be:

`f(9)=3(9)+15=42`
`g(9)=2(9)+30=48`

Therefore, after 9 years the chorus will have 42 people and the band will have 48 people.

D.

To find the number of years in which the number of people will be the same we equate the functions and solve for t:

`\begin{gathered} 3t+15=2t+30 \\ 3t-2t=30-15 \\ t=15 \end{gathered}`

Therefore, after 15 years the band and chorus will have the same number of people.