Exponential Functions in Context

The amount of bacteria in a sample after x hours can be represented by the function y = 200(3)^x. What does (3)^x mean in this context?

• There are 3 bacterium at the beginning

• The bacteria is tripling every hour

• The bacteria is increasing by 3% every hour

• The bacteria is decreasing by 3% every hour

The number of rabbits in Rabbit Forest can be modeled by the function R(x) = a₀(3)^x, where x is the time in years since the rabbits migrated there.

After five years, 1,458 rabbits are in Rabbit Forest. What was the initial population of rabbits?

• 3

• 4

• 5

• 6

What value of x makes this equation true?

4^x = 262,144

• 9

• 10

• 11

• 12

What function is represented by the sequence below? 7, 28, 112, 448 ...

• a_n = 4(7)^n-1

• a_n = 7(4)ⁿ

• a_n = 7(2)^n-1

• a_n = 7(4)^n-1

A guitar that costs $1,600 loses 7% of its value every year. What equation would model the value of the guitar, v, after t years?

• v = 1600(1.07)^t

• t = 1600(.93)^v

• v = 1600(.93)^t

• t = 1600(1.07)^v

The number of subscribers to Francisco's podcast after m months can be modeled by the function y = 150(1.09)^m. What is the growth rate of Francisco's listeners?

• 1.09

• 109%

• 90%

• 9%

The number of subscribers to Francisco's podcast after m months can be modeled by the function y = 150(1.09)^m. How many listeners would Francisco have after one year? (You can't have part of a subscriber)

• 163

• 421.9

• 421

• 163.5

What is the equation of the given graph?

• y = 2(2/3)^x

• y = 2(3/2)^x

• y = 2(1/2)^x

• y = (2)^x

How will the graph of y = 3^x translate when the function is changed to y = (3)^x-1+4?

• Shifted right 1 and up 4

• Shifted left 1 and down 4

• Shifted left 1 and up 4

• Shifted left 4 and up 1

• Shifted right 4 and up 1

Is the pictured graph growth, decay, or linear or none?  

• Exponential Growth

• Exponential Decay

• Linear

• None