Problem solving

Question

A number of years ago, the city planning department started a tree planting program to beautify the city. Below are data that show the total number of trees (in
Year===== 1988 1989 1990 1992 1995 1997
# of Trees==582 620 658 734 848 924

A. You are a member of the city planning department and your job is to decide if the department's plan to continue planting the same number of trees each year until the goal of a total of 5,000 trees was reached.

B. Assuming that no trees die, what should be the total number of trees in the city in the year 2020? Show how you found your answer.

C. In a 1989 newspaper article, the city claimed that it would have a total of 5,000 trees in the city by the time of the city's centennial celebration in the year 2088. If the planting of the new trees continues through the years at the same rate, can this goal be met? Justify your answer.

D. Write a short letter to the editor of the newspaper explaining your findings after examining the data. Be sure to support your claim with algebra.

Answer 1

Let's look at these trees again

 

Year     #trees

-----    --------

1988      582

1989      620

1990      658

1992      734

1995      848

1997      924

 

a)  The first thing we notice is that in each year, 38 trees were planted.  If in 1997, there are 924 trees in the city, at the rate of 38 trees planted per year, it will take more than 100 years to reach the goal of 5,000 trees.  This is derived by the following:

 

5000 - 924

------------ = 107.26 years. 

      38

 

Given that the project began in 1988, 10 years ago, per the data, it will take 117 years to reach the goal from the start.  Was this the expectation of the planning department?  It seems to be an extremely long period of time.  Is the goal even a realistic one.

 

b) in 2020, the number of trees will be

924 + 38(2020-1997) = 1,798 trees

 

c) the goal cannot be met.  It will be met in 2105.  See the comments in a).

 

I'll leave d) to you.  You can use the algebra in a) and b) above.