Question

There are 15 people in the chorus. Each year, the number of people in the chorus increases by 12%. There are 30 people in the band. Each year, 2 new people join the band.
Part A: Write functions to represent the number of people in the chorus and the number of people in the band throughout the years.

Part B: How many people are in the chorus after 9 years? How many people are in the band after the same number of years?

Part C: After approximately how many years is the number of people in the chorus and number of people in the band the same? Justify your answer mathematically.

Answer 1

Part A
Chorus:
Expontential growth = b*a^x 
b = 15
a = 1.12              (a= r+1), r = 12%

Which gives a function of f(x) = 15*1.12^x 


Band
Linear growth = ax+b
a = 2
b = 30

Which gives a function of g(x)=2x+30

Part B:
f(9) = 15*1.12^9 = 41.59
g(9) = 2*9+30 = 48

Part C:
This is probably problem solving, where you're allowed to use calculators and other softwares.

Therefore you can use different softwares, and make f(x) = g(x).
I did this, and got it to 10.95427141

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