Question

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 mathematica

Answer 1

For town A, increases of 20% per year are represented multiplication by (1.2) . Since you start with 30 homes, you will need this equation: \[30 \cdot (1.2)^y.\] For the town B, you have 45 homes that increase by 3 each year, you will need this equation \[45 + 3y.\]

Answer 2

For part B, you should plug in y = 5 into each of the equations. This will tell you how many homes the towns have.

For part C, set the two equations equal \[30 \cdot (1.2)^y = 45 + 3y\] and solve for y.