There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborhood B has 45
homes. Each year, 3 new homes are built in Neighborhood B. Part A: Write functions to represent the number of homes in Neighborhood A and Neighborhood B throughout the years.
Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years?
Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically.
Part A y=number of years (in both equations) F(a)=30(1+r/n)^y r=.2(20%) n=1
F(b)=45+(3y)
Part B A=74.6496 (personally I'd round to 74 because we are talking about an item that's not complete/useable yet, vs just a number if rounding is even required) B=60
Part C y=3.32 or approx 3 and 1/3 years solve both and each neighborhood has about 55 houses 54.95 for a 54.96 for b
A. this is assuming it grows by 20% of the houses it has at that time (compound interest) A(x)=30(1.2)ˣ⁻¹ or A(x)=25(1.2)ˣ B(x)=3(x-1)+45 or B(x)=3x+42
B. A(5)=62.28 or about 62 homes B(5)=60
C. this is tricky so I think it should have been only 20% of 30
start over
A. 20% of 30=6 A(x)=6(x-1)+30 or A(x)=6x+24 B(x)=3(x-1)+45 or B(x)=3x+42
B. A(5)=54 homes B(5)=60
C. 6x+24=3x+42 minus 3x 3x+24=42 minus 24 both sides 3x=18 divide by 3 x=6
