A bird species in danger of extinction has a population that is decreasing exponentially left parenthesis upper a equals upper a 0 e superscript kt right parenthesis . six years ago the population was at 1400 and today only 1000 of the birds are alive. once the population drops below 100 , the situation will be irreversible. when will this happen

This will happen in 39 years.

Explanation:

The population of the birds varies as A = A.e^kt

The population of birds fell from 1400 from 1000

Time it will take for the population to fall below 100 = x years.

when t = 0, population = 1400

t= 3; Population = 1000

Therefore:

1400 = 1000e^5k

e^5k= 1400/1000

k= (In 1.4)/5

we need to find x, such that

1400/1000= (e^xk)

14=(e^xk)

In(14) =kx

x= 5In(14)/In(1.4)

x= 39 years

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