How Much Revenue?
The new start-up is thriving! More and more customers are trying out the products,
leading to increased sales. The company made $20,000 in revenue in their first month,
and this amount is growing by 3% each month.
common ratio
1. Complete the table.
r=1 -03
Revenue ($)
Month 1
20,000
(20/000)=20,6002×1-03
Month 2
290001-0.03
Month 3
20,6001-0.03 (20/600)=21,218
Month 4
21,2181-0.03 (21,2/8)=21,854.54
2 ✗ I -03
Geometric
pot
2×1.03
2. Is the revenue increasing by the same dollar amount each month? How do you know?
NO , there is not a constant difference Between
land 2 the revenue increases by $600 but
Month
,µmeÑ
$618
between z and 3 revenue increases
3. Write a recursive rule to figure out the new month’s revenue if you know the previous
month’s revenue.
t
=
a __ 20,000
an , ( 0.03
An
.
µ
.
An
=
an ,
by
•
-
an
r
-
,
)
-
,
an -_ 1.03 Ian
-
4. Predict the company’s revenue in month 11. Show your method.
a ,, =
$26,878.33
5. A graph of the monthly revenue is shown. Add your ordered pairs from the table. What
r)
(
,
""
=
do you notice about the shape of the graph?
It's
curved
.
Arithmetic
Geometric
.
.
.
.
=
=
linear
curved
(exponential
Months
p= ,
)
20,0004-037%1,854.54 ✗ 1.03×1.03×1.03 ✗ 1.03×1.03×1.03×1.03
Revenue ($)
an=a
,
6. Suppose that after many months, the company’s revenue starts decreasing by 3%. How
would this affect your calculations?
the 3% of the previous
Instead of
-0.03
0.97
=
adding
month
you
would
subtract it
.
)
Lesson 1.4 – Applications of Geometric Sequences
QuickNotes
Geometric
geometric
r > s
an
an -1
r
an = a ,
•
(r)
geometric
decay
Explicit
•
ratio
a common
ocrc ,
growth
Recursive :
=
have
sequences
""
r
"
or
an
=
Go
•
r
!
Repeated multiplication → exponent
Check Your Understanding
1. Quinten has a secret. On the first day of school, he tells his closest friend. On the
second day, they each tell the secret to someone else. Each person that hears the
secret shares the secret with a new person each day.
a. How many people will know the secret on the 4th day of school?
Day_☒#
people
16 people
8
4
16
b. If on the 10th day of school, 1024 people know the secret, how many will know
the secret by the 11th day?
tells one
2048 because each personmore
person
c. Write an explicit rule for the number of students who know the secret on day n.
2
an =
2h
2. Which of the following are an example of geometric decay? Choose all that apply.
______ A bank account earns 1.25% interest annually
( geometric growth )
______A shirt is on sale for 15% off. ( not a sequence )
✓ swimmer reduces his 50-m backstroke by 2% each week of the summer
______A
______A teacher hands out 2 pencils every day
( arithmetic)
3. Could this table of values represent a geometric sequence? Why or why not?
1
18
!
"!
No ,
2
24
3
32
4
42
5
54
¥43 ¥73 ¥-325
there is not
a
common
ratio
.
4. A new iPhone is purchased for $799. The value of the iPhone decreases by 33% each
year. How much is the iPhone worth 5 years after it was purchased?
799
•
( 0.67 )s=
$107.87