At the beginning of each year in Guelph\'s arboretum, biologists add 1,000 frogs

Question

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:

where Xn is the population of frogs at the beginning of year n. What are the values for a and b?

Select the correct answer from the options below:

1) a=0.95, b=950

2) a=0.05, b=950

3) a=5, b=1000

4) a=0.95, b= 1000

5) a= 0.05, b=900

6) a= 0.05, b=1000

7) a= 1000, b= 5

8) a=0.95, b= 900

9) a= 1000, b = 0.95

10) a=950, b= 0.95

Explanation / Answer

Option 4) a= 0.95, b= 1000

Given that he is adding 1000 at the beginning and it's independent from n hence b= 1000

And harvesting 5% means remaining = 100-5 = 95% = 0.95

Hence a = 0.95

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