06-01_task
pdf
keyboard_arrow_up
School
Virgil I. Grissom High School *
*We aren’t endorsed by this school
Course
MATH
Subject
Mathematics
Date
Nov 24, 2024
Type
Pages
2
Uploaded by ElderNeutron3900
Name:
Jesus Hernandez
Date:
12-31-2023
School:
Grissom High School
Facilitator:
Mrs. Walker
6.01 Exponential Growth and Decay (55
Points)
Rabbits reproduce quickly. If an area starts with a rabbit population of 5 and the
population doubles every month, what will be the population after 6 months and how long
will it take for the population of rabbits to exceed 500 total rabbits?
1. Fill in the table of values to determine the answer.
months
0
1
2
3
4
5
6
7
8
9
number
of
rabbits
5
10
20
40
80
160
320
640
1,280
2,560
2. Finish the statement: After 6 months, the population of rabbits is
around 6 months making
it’s 320 but after it’s 640.
.
3. Create an equation to represent the population of rabbits: y =
5
(
2
)
t
4. How long will it take for the population of rabbits to exceed 500 total rabbits?
It would take
around or between 6 to 7 months.
A social network (eMathGeeks) gets 200 new users in its first month of use, January. If the
number of new users triples each month, how many new users will join in May? How many
months will it take for it to have 1 million members?
5. Fill in the table of values to determine the answer.
Jan
Feb
March
April
May
June
July
Aug
Sept
Oct
months
0
1
2
3
4
5
6
7
8
9
number
of new
users
200
600
1,800
5,400
16,200
48,600
145,800
437,400
131,220
3,936,600
6. Finish the statement: The number of new users in May is
16,200
.
7. Create an equation to represent the number of months that it will take to have 1 million
members: y =
200
(
3
)
t
8. How many months will it take for eMathGeeks to have 1 million members?
It would take
between 7 or 8 months.
Sales of a new tablet grow by 10% every month. Sales for this month are at 5 thousand.
Write an equation to represent this situation and then approximate the sales 6 months from
now.
9. This problem will use the equation A(t) = a(1 + r)
t
. Identify a, r, and t.
a =
5,000
r =
0.10
t =
6
10. Find the sales 6 months from now. Show your work.
5000(1.17)
© ACCESS Virtual Learning 2021
=8857.8
While sales of tablets increase, sales of game systems are falling. If the sales of games
systems are at 5 million in 2012 and fall by 25% each year, how many game systems will be
sold in 2015?
11. This problem will use the equation A(t) = a(1 - r)
t
. Identify a, r, and t.
a =
5,000,000
r =
0.25
t =
3
12. Find the number of units sold in 2015. Show your work
5,000,000 (.4218)
=2,109,375 units
A population of 10,000 mice is infected by a virus. Initially, 20 mice are infected. If the
number of infected mice doubles each day, how long will it take for half of the mice to be
infected?
13. Make a t-chart
Day
Number of mice
infected
1
20
2
40
3
80
4
160
5
320
6
640
7
1,280
8
2,560
9
5,120
10
10,240
14. Plot the points from the graph (you can use the Shapes tool to make points).
15. How long will it take for more than half of the mice to be infected?
It would take about 9
days in a half for the mice to be infected.
© ACCESS Virtual Learning 2021
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help