Algebra 1 Help! Will Fan and Medal!

Question

anonymous · Answer

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. (4 points)
Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years? (2 points)
Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically. (4 points)

lukeskylicker · Answer

First off I spot test question.

janu16 · Answer

Part A: Write functions to represent the number of homes in Neighborhood A and Neighborhood B throughout the years. (4 points)
y = 30 (1.2)^x
y= 45 + 3*x
Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years? (2 points)
30(1.2)^5= 74.65
45 + 3*5=  60
Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically.
solve 
30 (1.2)^x =  45 + 3*x
using a graphing calculator i got 
x = 3.32079
in the third year the number of homes are the same

lukeskylicker · Answer

Second of all I will explain to you how to get the answers for Part A through C but not any actual answers.

Part A: y will equal the number of homes so we have  y = that will be the beginning of both answers. Afterwards there will be the constant (the total number of homes when x is equal to zero) and the amount increasing the total when x is equal to a positive number. Remember though. If the equation is increasing linearly do x (the year) times the amount number your given (or put another way, if your given an integer use multiplication) but if it's increasing exponentially have the number (which should be a percentage) to the power of x or $$y^x$$

Part B: take the equation from Part A and replace all instances of x with 5.

Part C: input your functions into a graphing calculator or use desmos.com

anonymous · Answer

Thank you.