Question

The population of Humpback whales was once thought to be as high as 125 000, although this number was drastically reduced due to whaling. New whaling laws have allowed the population to increase again. Since 1979, the population has experienced exponential growth that can be modeled by the equation P = 7500(1.031)n, where P represents the population, and n represents the years since 1979. ( i.e. for 1979, n = 0)
a. Use the equation to estimate the population in the years 1979, 1985, and 1995.
b. According to the mathematical model, in what year will the population reach 20,000 whales?
c. Give reasons why this model may not accurately predict the future population.

Answer 1

Answer:

oops too lengthy

i don't wanna read

Answer 2

Answer:

a. The population of whales in 1979 = 7500

   The population of whales in 1985 = 9007

   The population of whales in 1995 = 12223

b. The population reached 20,000 whales in 2011.

c. This model, the population only shoots up and there is no saturation point which is not a accurate representation of a population behavior.

Step-by-step explanation:

The exponential growth of Humpback whales population from 1979 is given by the equation

P =$7500(1.031^{n} )$   .........(1)

where, n is the number of years since 1979, n = 0 for 1979

            P is the population

a. The population of whales in 1979, 1985, 1995.

To find the population in these three years, we should know the number of years between the target year and 1979, that is the value of n.

1979: n = 0

1985: n = 6

1995: n = 16

By substituting the values of n in (1), the population can be calculated.

The population of whales in 1979 = 7500

The population of whales in 1985 = 7500(1.031^6) = 9007

The population of whales in 1995 = 7500(1.031^16) = 12223

b. In what year will the population reach 20,000 whales?

To find out the year, we should find the number of years from 1979 when the population is 20,000 that is the value of n when P is 20000.

20000 = 7500(1.031^n)

1.031^n   =  2.666

n = 32

After 32 years from 1979, the population of whales reached 20000.

The population reached 20,000 whales in 2011.

c. Because as n increases, more and more the value shoots up very high which is not the case for real life population scenario. As generally, the population curves are supposed to look like a bell curve. So this model may not accurately predict the future population.

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