Geometric Sequences and Exponential Growth and Decay

If a table's pattern is that the f(x) values are being divided by 3, what is the common ratio?

• 3

• -3

• 1/3

• -1/3

Identify the next three terms in the geometric sequence. 
8, 24, 72, 216, ...

• 512, 1024, 4832

• 648, 1944, 3888

• 512, 1536, 4608

• 648, 1944, 5832

Identify the next three terms in the geometric sequence. 
1, -1/3, 1/9, -1/27,...

• -1/81, 1/243, -1/729

• 1/81, -1/243, 1/729

• -1/54, 1/81, -1/243

• 1/54, -1/162, 1/486

The first term of a geometric sequence is 400 and the common ratio is 0.5. What is the 5^th term of the sequence?

• 100

• 50

• 25

• 5

The 12th term of the sequence is
3, -9, 27, -81, 243,...?

• 531,441

• 177,147

• -177,147

• -531,441

The table shows the value of a townhome for 3 years after it is purchased. The values form a geometric sequence. If the pattern continues, how much will the townhome be worth after 7 years?

• $457,763.67

• $457,633.12

• $452,000.00

• $366,210.93

The value of a sculpture is increasing 5% every month. The original value of the sculpture is $6,400. Identify the exponential growth function to model this situation.

• y = 6400(1.5)^t

• y = 6400(1.05)^t

• y = 6400(0.95)^t

• y = 6400(15)^t

The population of an endangered species of insect is 480,000. The population decreases at the rate of 10% per year. Find the population of the species after 3 years. 

• 280,000

• 638,880

• 339,940

• 349,920

What kind of sequence is the pattern 400, 200, 100, 50, 25, ...?

• Arithmetic

• Geometric

• Neither

Write an equation that models the following situation: Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week. (HINT: Write out the equation on a separate piece of paper and hen simplify inside the parenthesis)

• y=6(0.14)^x

• y=6(1+14)^x

• y=6(1.14)^x

• y=6(0.86)^x