Section 8A Practice

The balance owed on your credit card doubles from ​$2000 to ​$4000 in 3 months. If your balance is growing​ exponentially, how much longer will it be until it reaches ​$8000​?

• It will be 3 months because the balance doubles every months, and $8000 is twice as much as $4000

• It will be 6 months because the balance increases by $3000 every 3 months.

• It will be 9 months because the balance increases by $2000 every 3 months, and $8000 is $6000 more than $2000.

• It will be 9 months because $2000 has to double three times to become $8000.

Which of the following is an example of exponential decay?

• The population of a rural community decreasing by 100 people per year is an example of exponential decay because population growth and decay are represented exponentially, and in this case it is decreasing.

• The price of gasoline decreasing by $0.02 per week is an example of exponential decay because the price decreases very slowly at first.

• The price of gasoline decreasing by $0.02 per week is an example of exponential decay because the amount at which the price is decreasing increases by $0.02 each week.

• Government support for education decreasing by 1% per year is an example of exponential decay ecause the support decreases by the same percentage each year.

Explain your reasoning with one or more complete sentences. At 11:00 you place a single bacterium in a bottle, and at 11:01 it divides into 2 bacteria, which at 11:02 divide into 4 bacteria, and so on. How many bacteria will be in the bottle at 11:30?

• There will be 2X30 bacteria in the bottle because there are 2 bacteria after the first minute, and the number of bacteria increases over 30 minutes.

Tags

CCSS.HSF.BF.A.2

At 11:00 you place a single bacterium in a bottle, and at 11:01 it divides into 2 bacteria, which at 11:02 divide into 4 bacteria, and so on. If the bacteria occupy a volume of 1 cubic meter at 12:02 and continue their exponential growth, when will they occupy a volume of 2 cubic meters?

• 1:02

• 12:03

• 1:03

• 12:04

Tags

CCSS.HSF.LE.A.4

Describe the basic differences between linear growth and exponential growth.

• Linear growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time, and exponential growth occurs when a quantity grows by the same absolute amount in each unit of time.

• Linear growth occurs when a quantity grows by the same absolute amount in each unit of time, and exponential growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time.

• Linear growth occurs when a quantity grows by different, but proportional amounts, in each unit

  of time, and exponential growth occurs when a quantity grows by random amounts in each unit of time.

• Linear growth occurs when a quantity grows by random amounts in each unit of time, and exponential growth occurs when a quantity grows by different, but proportional amounts, in each unit of time.

Briefly summarize the story of the bacteria in a bottle

• The number of bacteria in a bottle triples every minute. There is one bacteria at 11:00 and the bottle is full at 12:00, so the colony is doomed

• The number of bacteria in a bottle increases by 2 every minute. There is one bacteria at 11:00 and the bottle is full at 12:00, so the colony is doomed.

• The number of bacteria in a bottle doubles every minute. There is one bacteria at 11:00 and the bottle is full at 12:00, so the colony is doomed.

• The number of bacteria in a bottle increases by 1 every minute. There is one bacteria at 11:00 and the bottle is full at 12:00, so the colony is doomed.

Why was the bottle half-full at 11:59?

• The bottle was half-full at 11:59 because the number of bacteria doubles during the last minute.

• The bottle was half-full at 11:59 because the volume of bacteria exceeds the volume of the bottle at 12:00.

• The bottle was half-full at 11:59 because the bacteria stop dividing before the bottle becomes completely full.

• The bottle was half-full at 11:59 because the bottle is half-full at 11:30, and 11:59 is after 11:30.

Why won't the other bacteria believe you about the impending disaster?

• The other bacteria won't believe you because 15/16 of the bottle is still unoccupied at 11:56.

• The other bacteria won't believe you because 3/4 of the bottle is still unoccupied at 11:56.

• The other bacteria won't believe you because the rate at which the bacteria are dividing will cause less than 10% of the bottle to be occupied by 11:59.

• The other bacteria won't believe you because the rate at which the bacteria are dividing will cause less than 1% of the bottle to be occupied by 11:59.

Tags

CCSS.5.NF.B.5B

Why does the discovery of the 3 new bottles give the bacteria only 2 additional​ minutes?

• The discovery gives only 2 additional minutes because each of the 3 new bottles takes 40 seconds to fill, and the first bottle is already full.

• The discovery gives only 2 additional minutes because the bacteria consistently fill 2 bottles per minute.

• The discovery gives only 2 additional minutes because it will take half of a minute to fill each bottle, for a total of 2 minutes.

• The discovery gives only 2 additional minutes because the bacteria will fill 2 bottles by 12:01 and 4 bottles by 12:02.

Money in a bank account earning compound interest at an annual percentage rate of 3% is an example of exponential growth.

• True because the money in the account grows by the same absolute amount, which is an example of exponential growth.

• False because the money in the account grows by the same absolute amount, which is an example of linear growth.

• True because the money in the account grows by the same percentage, which is an example of exponential growth.

• False because the money in the account grows by the same percentage, which is an example of linear growth.

Tags

CCSS.HSF-IF.C.8B