Exponential Functions Plug In

What is it about the equation y = 2(9/7)^x that indicates that it is a model for exponential growth?

• The equation is growth because 2 is positive.

• The equation is growth because the factor is positive.

• The equation is growth because the factor is greater than one.

• The equation is growth because the exponent is always positive.

Consider the equation y=200(1.08)^x which models the increase in value of an autographed Annie program. Let y = the value of the item, let x = the number of years since the performance. What does the 1.08 in the equation indicate?

• The value of the item is increasing by $1.08 each year.

• The value of the item is increasing by 1.08% each year.

• The value of the item will increase to $200 1.08 years after purchase.

• The value of the item is increasing by 8% each year.

If you were asked to write an exponential function with an asymptote of y = - 2, what must you include in your equation?

• Subtract 2 from any exponential expression. Ex. y = (4)^x - 2

• Add 2 to any exponential expression. Ex. y = (4)^x + 2

• Raise the expression to the power of -2. Ex. y = x ^-2

• Subtract .02 from 1 to get a decay factor. Ex. y = (1 - .02)^x

A population of mutant venus fly trap plants are taking over an island in the South Pacific, capturing everything from insects to small rodents. When they were first discovered they covered 4 square kilometers. As the population grows, the plants spread and cover more land. How many years will it take for the plants to occupy 400 km²?

• 8 years

• 9 years

• 10 years

• 11 years

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month. At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?

input

A sample of a substance with an initial mass of 500 grams is decaying at a rate of 32% per hour. 

 

Create a function that can be used to find y, the mass of the substance in grams remaining after x hours.

 

Enter your answer in the space provided.

Mathematical Equivalence

ON

A shipping company started with 40 employees. The number of employees in the shipping company increases at a rate of 7.5% each year. What function can be used to model the number of employees, f(x), in the shipping company after x years?

Which equation matches the graph?

• y = 2^x+3

• y = 2^x + 3

• y = 2^x

• y = 2^-x

Create the exponential function with the following attributes:

Asymptote: y = 0

Initial value: 3

Point on the graph: (2, 6)

Growth