Question

In: Advanced Math

in 2013 the estimated world population 7.1 billion use the doubling of 70 years to predict...

in 2013 the estimated world population 7.1 billion use the doubling of 70 years to predict the population 2027, 20153 and 2103?

Expert Solution

For year 2013 assume t = 0.

Hence 70 years after 2013 becomes t = 70.

At t= 0, P = 7.1 billion.

At t = 70, P = (7.1)*2 = 14.2 billion.

Let

Where is the initial population, t is time in year, r is rate of growth.

Substitute P(0) = 7.1 and simplify right side, get

Resubstitute in , get

Now substitute t = 70 and P(70) = 14.2 get

Divide both sides by 7.1 get

Take natural logarithm function from both sides,

Using ln (a^n) = n*ln(a)

ln(2) = 70r * ln(e)

Since ln(e) = 1

ln(2) = 70r

r = 0.009902102579

1) To popuation in 2027 that is to p when t = 14.

Plug t= 14 in , get P = 8.15551 billion.

2) To find population is 20153 , plug t= 150 in get p=31.34625billion.

3) To find population in 2103 , plug t = 90 in get p= 17.30671 billion.

Colby Messinger answered 2 years ago

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