Logistic and Exponential Models

What does the y-intercept of the graph represent?

• The amount of grams the material is gaining.

• The amount of grams the material is losing.

• The amount of grams remaining after so many years.

• The initial amount of grams.

Which of the following is an increasing exponential function whose y-intercept is 50?

• y = 50(.05)^x

• y = 50x - 4

• y = (2)^x + 50

• y = 50(1.4)^x

The amount of ants in a colony, f, that is decaying can be modeled by                         f(x) = 800(.87)^x, where x is the number of days since the decay started. Suppose           f(20) = 49. Which of the following is true?

• After 20 days, there are 49 ants in the colony.

• After 49 days there are 20 ants in the colony.

• The amount of ants times 20 is 49.

• After 20 days the amount of ants remaining decreases by 49.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 12 represent?

• The predicted increase in number of elephants in the refuge each year.

• The predicted decrease in number of elephants in the refuge each year.

• The number of years it will take for the elephant population to stop increasing.

• The initial amount of elephants in the park.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 1.015 represent?

• The number of elephants was 1,015 in 1975.

• The number of elephants increases by 1.5% each year.

• The number of elephants increases by 101.5% each year.

• The number of elephants is multiplied by 1.015 each year.

Is the graph exponential growth or decay?

• Exponential growth

• Exponential decay

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

• 300

• 1.16

• .16

• x

In an exponential function, what does the 'b' represent? 

• SLOPE

• RATE OF CHANGE

• INITIAL AMOUNT

• GROWTH OR DECAY  FACTOR

What is the carrying capacity for this sheep population?

• 8 million

• 25 million

• 6 million

• o million

What is the carrying capacity of this population?

• 100

• 200

• 300

• 400