431 words - 2 pages

GROWTH & DECAY WORKSHEET – SOLUTIONS

PAPER 2: CALCULATOR

1. A population of 120 mammals from an endangered species was introduced onto an enclosed reserve at the start of 1990. By the start of 1995, the population had increased to 300.

It is believed that a model of the form, (where N (t) represents the number of mammals present at time t years since their introduction onto the reserve) adequately approximates the population size of this mammal.

a) State the value of . What does it represent?

No. is 120. That is the number of species at the “beginning” in 1990.

b) Determine the value of k to 4 decimal places.

c) Find the population size in the year 2000.

d) When will the population reach a size of 1000?

2.

The number of field mice, N, in an area in which the coyotes have all been killed by humans can be modeled by the function, where t is the number of years from now.

a) When will the population of field mice grow to 4000?

b) When will the population of field mice triple?

3.

The number, N, of rare and little-studied forest elephants in an area of central Africa that is being denuded of trees can be modeled by the function, where t is ...

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