Question

The current population of England is 500,000 people in England has had a constant percent growth rate of 10% in 1985 in which year was the population of England Amir 125,000 people show your work so let’s assume that birthweight doubled while death rate did not change determine whether following values would increase decrease or stay the same growth rate Percentage

Answer 1

To determine in which year the population of England was approximately 125,000 given a constant growth rate of 10% since 1985 when the population was 500,000, we can use the formula for exponential growth:

\[ P = P_0 (1 + r)^t \]

Where:

• \( P \) is the future population,
• \( P_0 \) is the initial population,
• \( r \) is the growth rate (as a decimal),
• \( t \) is the time in years.

Given:

• \( P = 500,000 \) (population in 1985)
• \( r = 0.10 \) (10%)
• We need to find \( t \) at which \( P \) equals 125,000.

Rearranging the equation and substituting for \( P \):

\[ 125,000 = 500,000 (1 + 0.10)^{-t} \]

Now divide both sides by 500,000:

\[ \frac{125,000}{500,000} = (1.10)^{-t} \]

This simplifies to:

\[ 0.25 = (1.10)^{-t} \]

Taking the natural logarithm of both sides gives:

\[ \ln(0.25) = -t \ln(1.10) \]

Now we can solve for \( t \):

\[ t = -\frac{\ln(0.25)}{\ln(1.10)} \]

Calculating:

1. \( \ln(0.25) \approx -1.3863 \)
2. \( \ln(1.10) \approx 0.0953 \)

Now substituting these values in:

\[ t \approx -\frac{-1.3863}{0.0953} \approx 14.55 \]

This means that it took about 14.55 years for the population to grow from 125,000 to 500,000, starting from a given year of 1985:

Now subtracting this from 1985:

1. 14.55 years corresponds to approximately 15 years. Thus, we go back about 15 years from 1985.

2023 - 15 = 1970 (approximately).

Thus, the population of England was approximately 125,000 people around the year 1970.

Analysis of Growth Rate Percentage After Doubling Birth Rates

If we assume that the birth rate doubles while the death rate remains unchanged, the growth rate (percentage) of the population will:

• Increase: Since the birth rate is increasing, the overall population growth rate will also increase. Births contribute positively to population growth, while the unchanged death rate will not counteract this increase.

In summary:

• The population of England was approximately 125,000 in around the year 1970.
• The growth rate percentage would increase as a result of the birth rate doubling while the death rate remains unchanged.