Certainly! Let's calculate the estimated world population for the year 2050 given the initial conditions. Here's a step-by-step explanation:
### Step-by-Step Solution:
1. Initial Population (2014):
The initial population in 2014 is given as 7 billion. Let's denote this as [tex]\( P_0 \)[/tex]:
[tex]\[
P_0 = 7,000,000,000
\][/tex]
2. Annual Growth Rate:
The annual growth rate is given as 1.19%. To use this in our calculations, it needs to be converted from a percentage to a decimal:
[tex]\[
r = \frac{1.19}{100} = 0.0119
\][/tex]
3. Number of Years:
We are interested in calculating the population for the year 2050, starting from 2014. The number of years ([tex]\( t \)[/tex]) will be:
[tex]\[
t = 2050 - 2014 = 36
\][/tex]
4. Population Growth Formula:
The formula to estimate the future population given an initial population, growth rate, and number of years is:
[tex]\[
P_t = P_0 \times (1 + r)^t
\][/tex]
where [tex]\( P_t \)[/tex] is the population at time [tex]\( t \)[/tex].
5. Calculation:
Plugging the values into the formula:
[tex]\[
P_{2050} = 7,000,000,000 \times (1 + 0.0119)^{36}
\][/tex]
Simplifying the expression inside the parentheses first:
[tex]\[
1 + 0.0119 = 1.0119
\][/tex]
Raising this to the power of 36:
[tex]\[
(1.0119)^{36}
\][/tex]
Then multiplying by the initial population:
[tex]\[
P_{2050} = 7,000,000,000 \times (1.0119)^{36}
= 7,000,000,000 \times 1.531184427
\][/tex]
Finally, we get:
[tex]\[
P_{2050} = 10,716,463,589.564
\][/tex]
### Conclusion:
The estimated world population in the year 2050, based on an initial population of 7 billion in 2014 and an annual growth rate of 1.19%, will be approximately 10,716,463,589.
So, the world population in 2050 is expected to be around 10.72 billion.
