Question

In April 2015 in the US, there was one birth every 8 seconds, one death every 12 seconds, and one new international migrant every 32
seconds
(a) Letf(t) be the population of the US, wheret is time in seconds measured from the start of April 2015.
Findf'(o).
Round your answer to four decimal places.

Answer 1

The growth rate of a population is the rate at which the population changes

The rate of change is 0.0729 people per second

Let:

b represents birth

d represents death

m represents migrant

So, the given parameters are:

$\mathbf{b = \frac 18\ people/sec}$

$\mathbf{d = -\frac 1{12}\ people/sec}$

$\mathbf{m = \frac 1{32}\ people/sec}$

The negative sign represents death

So, the population change f'(o) every second is:

$\mathbf{f'(o) = b + d + m}$

This gives

$\mathbf{f'(o) = \frac 18 - \frac{1}{12} + \frac 1{32}}$

Take LCM

$\mathbf{f'(o) = \frac{12 - 8 + 3}{96}}$

$\mathbf{f'(o) = \frac{7}{96}}$

Divide

$\mathbf{f'(o) = 0.072916}$

Approximate

$\mathbf{f'(o) = 0.0729}$

Hence, the rate of change is 0.0729 people per second

Read more about population growth at:

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