Michael is recruiting students on his college campus to join a disaster relief team to provide support to those affected by natural disasters such as hurricanes, floods, earthquakes, etc.

During the first week he works to recruit members to the disaster relief team, so that by the beginning of Week 2 there are three new members. Those three new members each recruit three others, for a total of nine new members by the beginning of Week 3. The pattern continues so that every new member recruits three others the following week. A member is only considered a “new” member for the one week they are recruiting three others.

If the pattern continues, at the beginning of what week will exactly 729 new members join the disaster relief team? (Demonstrate your solution algebraically and graphically.)

Step 1: Complete the table and write a function (Hint: Choose one of these forms to help you

write your exponential function)

a = zero term of the sequence (y-int)

b = common ratio

Geometric Sequence

 

# Weeks	# New Volunteers
1
2
3
4
5
6

Use the table to write an exponential function to model this situation:

Step 2: Sketch the Graph of your function below (Be sure to label and scale your axes!)

Step 3: Use the function/ table/ graph you constructed above to solve for the number of weeks when there will be exactly 729 new members. (SHOW YOUR WORK)

Step 4: Plot the point on your graph above that represents when there will be exactly 729 new volunteers. Write the point here in coordinate form (x,y) and answer the question: at the beginning of what week will exactly 729 new members join the disaster relief team?

Point:

Explanation:
 
 
 

Transcribed Image Text:

The standard form of an exponential equation is y = a.bx an= a₁.rn-1 where: an = nth term a₁ = 1st term r = common ratio The standard form of an exponential equation is y = a.bx an= a₁.rn-1 where: an = nth term a₁ = 1st term r = common ratio