Answer :
To determine the population growth rate for a country that doubles its population in 56 years, we can use a concept from demography known as the "Rule of 70." This is a useful approximation that allows us to estimate the doubling time for a population given its growth rate, or vice versa.
The Rule of 70 states that the doubling time (T, in years) for a population can be approximated using the formula:
[tex]\[ T = \frac{70}{r} \][/tex]
where [tex]\( r \)[/tex] is the growth rate expressed as a percentage.
Given:
- The doubling time [tex]\( T \)[/tex] is 56 years.
We need to find the growth rate [tex]\( r \)[/tex]. We can rearrange the formula to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \frac{70}{T} \][/tex]
Substitute the given doubling time [tex]\( T \)[/tex] into the formula:
[tex]\[ r = \frac{70}{56} \][/tex]
Now, perform the division:
[tex]\[ r = \frac{70}{56} \approx 1.25 \][/tex]
So, the population growth rate [tex]\( r \)[/tex] is approximately 1.25%.
To summarize:
1. We used the Rule of 70 to relate the doubling time to the growth rate.
2. We rearranged the formula to solve for the growth rate.
3. We substituted the given doubling time of 56 years into the equation.
4. We calculated the growth rate to be approximately 1.25%.
Therefore, the population growth rate is approximately 1.25%.
The Rule of 70 states that the doubling time (T, in years) for a population can be approximated using the formula:
[tex]\[ T = \frac{70}{r} \][/tex]
where [tex]\( r \)[/tex] is the growth rate expressed as a percentage.
Given:
- The doubling time [tex]\( T \)[/tex] is 56 years.
We need to find the growth rate [tex]\( r \)[/tex]. We can rearrange the formula to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \frac{70}{T} \][/tex]
Substitute the given doubling time [tex]\( T \)[/tex] into the formula:
[tex]\[ r = \frac{70}{56} \][/tex]
Now, perform the division:
[tex]\[ r = \frac{70}{56} \approx 1.25 \][/tex]
So, the population growth rate [tex]\( r \)[/tex] is approximately 1.25%.
To summarize:
1. We used the Rule of 70 to relate the doubling time to the growth rate.
2. We rearranged the formula to solve for the growth rate.
3. We substituted the given doubling time of 56 years into the equation.
4. We calculated the growth rate to be approximately 1.25%.
Therefore, the population growth rate is approximately 1.25%.
