Question 1

At the beginning of each year in Guelph's arboretum, biologists add 1,000 frogs to the population and at the end of the year, biologists harvest 5% of the population. Let the difference equation that models this population be given by:

X_n+1=aX_n+b

whereX_nis the population of frogs at the beginning of yearn. What are the values foraandb?

Question 1 options:

a=1,000, b=0.95

a=0.05, b=950

a=0.95, b=1,000

a=0.05, 1,000

a=950, b=0.95

a=0.95, b=900

a=0.05, b=900

a=1,000, b=5

a=0.95, b=950

a=5, b=1,000

Question 2

Let ?X_n=?0.5X_n+100, where X₀=5,000.

Let the solution be given by A+B(C)ⁿ.

What are the values of A, B and C?

Question 2 options:

A=500, B=4,500, C=0.8.

A=2,000, B=3,000, C=0.05.

A=400, B=4,600, C=0.75.

A=200, B=4,800, C=0.5.

A=400, B=4,600, C=0.25.

A=2,000, B=3.000, C=-0.5.

A=500, B=4,500, C=0.2.

A=1,000, B=4,000, C=0.9.

A=2,000, B=3,000, C=0.95.

A=1,000, B=4,000, C=0.1.

Question 3

Use the following graph of a difference equation to estimate the value ofx₃, givenx₁=1.25.

The value ofx₃is estimated to lie in the interval: ___

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