413. A country's population is growing at a rate of 2% per year. If the current population is 1 billion, what will be the population after 10 years? (Use the formula for exponential growth: $P = P_0(1 + r)^t$ where $P_0$ is initial population, $r$ is growth rate, and $t$ is time in years.)
Key Concept: Population growth, contraceptive methods
b) 1.219 billion
[Solution Description]
To calculate the population after 10 years, we use the exponential growth formula:
$P = P_0(1 + r)^t$
Here,
- $P_0 = 1,000,000,000$ (1 billion)
- $r = 2% = 0.02$
- $t = 10$ years
Substituting the values:
$P = 1,000,000,000(1 + 0.02)^{10} = 1,000,000,000(1.02)^{10}$
Calculating $(1.02)^{10}$:
$1.02^{10} \approx 1.21899442$
Now multiply by $P_0$:
$P \approx 1,000,000,000 \times 1.21899442 = 1,218,994,420$
So, the population after 10 years is approximately 1.219 billion.
Your Answer is correct.
b) 1.219 billion
[Solution Description]
To calculate the population after 10 years, we use the exponential growth formula:
$P = P_0(1 + r)^t$
Here,
- $P_0 = 1,000,000,000$ (1 billion)
- $r = 2% = 0.02$
- $t = 10$ years
Substituting the values:
$P = 1,000,000,000(1 + 0.02)^{10} = 1,000,000,000(1.02)^{10}$
Calculating $(1.02)^{10}$:
$1.02^{10} \approx 1.21899442$
Now multiply by $P_0$:
$P \approx 1,000,000,000 \times 1.21899442 = 1,218,994,420$
So, the population after 10 years is approximately 1.219 billion.