Geometric Sequences and Exponential Growth and Decay

Find the common ratio for the geometric sequence.

• -4

• 4

• 1/4

• -1/4

Find the next three terms of the geometric sequence: 4, 12, 36, 108, ...

• 324, 972, 2916

• 972, 2916, 8748

• 405, 1215, 3645

Which formula is used to find the explicit equation for geometric sequences?

• a_n = a_n-1 + d

• a_n = a_n-1 * r

• a_n = a₁ + d(n-1)

• a_n = a₁ * r^n-1

Emily is culturing bacteria that have a growth rate of 5% per hour. If the current population is 36,000 bacteria, how many bacteria will there be in 12 hours? If necessary, round your answer to the nearest whole number.

• 8,789,062 bacteria.

• 19,452 bacteria.

• 61,572 bacteria.

• 64,651 bacteria.

• A

• B

• C

• D

A newly launched clothing line is rapidly increasing in popularity. Every month, 20% more items of clothing are sold. If 89,090 items were sold this month, how many will be sold in 9 months from now? If necessary, round your answer to nearest whole number.

• 74,278 items.

• 11,957 items.

• 319,226 items.

• 459,685 items.

How many fruit flies are in the population after 7 days (1 week)?

• 140 flies

• 105 flies

• 101 flies

• 735 flies

The population of a school is 2200 and is increasing at a rate of 2% each year. Find the population after 6 years.

The attendance at the art museum at the New Year’s opening was 300 people. The attendance has been increasing at a rate of 5% each month. How many people will attend by the end of a year?

*Answer with the number value only

**Round appropriately

This is an example of.....

• exponential decay

• exponential growth

• constant change

• a linear function