Question

# A bird species in danger of extinction has a population that is decreasing exponentiallyA=A_0 e^(kt).Five 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?

Equations and inequalities

A bird species in danger of extinction has a population that is decreasing exponentially
$$A=A_0 e^{kt}$$.
Five 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?

## Expert Answers (1)

2021-02-20

The population of birds vary as $$A=A_0 e^{kt}$$
Given that population of brds fell from 1400 to 1000,we are asked how much time it will ake forthe population to fall below 100 when t=5
we can write the following equation
$$1400=1000e^{5k}$$
$$k=(1.4)/(5)$$
we need to find x,such that $$(1400)/(100)=(e^x k)$$
$$14=(e^{xk})$$
in (14)=kx
$$x=(5 \in (14))/(\in(1.4)) \approx 39$$ years
It will take 39 years for the population f birds to fall below 100