A logistic growth model for world population, , in billions, years after 1983 is
According to this model, when will the world population be 12 billion?
According to this model, the world population will be 12 billion in
(Round to the nearest whole number as needed.)

Ask by Brooks Hill. in the United States

Mar 31,2025

Question

A logistic growth model for world population, , in billions, years after 1983 is
According to this model, when will the world population be 12 billion?
According to this model, the world population will be 12 billion in
(Round to the nearest whole number as needed.)

Ask by Brooks Hill. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

We start with the logistic model

$$
f(x)=\frac{12.57}{1+4.11e^{-0.026 x}},
$$

and we want to find $$ x $$ such that $$ f(x)=12 $$. That is,

$$
\frac{12.57}{1+4.11e^{-0.026 x}}=12.
$$

1. Multiply both sides by $$ 1+4.11e^{-0.026 x} $$:

$$
12\left(1+4.11e^{-0.026 x}\right)=12.57.
$$

2. Divide by 12:

$$
1+4.11e^{-0.026 x}=\frac{12.57}{12}=1.0475.
$$

3. Isolate the exponential term:

$$
4.11e^{-0.026 x}=1.0475-1=0.0475.
$$

4. Divide by 4.11:

$$
e^{-0.026 x}=\frac{0.0475}{4.11}\approx0.01156.
$$

5. Take the natural logarithm of both sides:

$$
-0.026x=\ln(0.01156).
$$

6. Solve for $$ x $$:

$$
x=\frac{-\ln(0.01156)}{0.026}.
$$

Calculating the natural logarithm,

$$
\ln(0.01156)\approx-4.460,
$$

so

$$
x\approx\frac{4.460}{0.026}\approx171.54.
$$

Rounding to the nearest whole number gives $$ x\approx172 $$ years after 1983. Thus, according to the model, the world population will be 12 billion in

$$
1983+172=2155.
$$
According to the model, the world population will be 12 billion in the year 2155.

A logistic growth model for world population, , in billions, years after 1983 is
According to this model, when will the world population be 12 billion?
According to this model, the world population will be 12 billion in
(Round to the nearest whole number as needed.)

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Pre Calculus Questions

A logistic growth model for world population, , in billions, years after 1983 is According to this model, when will the world population be 12 billion? According to this model, the world population will be 12 billion in (Round to the nearest whole number as needed.)

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Pre Calculus Questions

A logistic growth model for world population, , in billions, years after 1983 is
According to this model, when will the world population be 12 billion?
According to this model, the world population will be 12 billion in
(Round to the nearest whole number as needed.)