Question

In how many years will the population of a colony be 92,610 from 80,000 at the population growth rate of 5% per annum? If the growth rate is 2% less than before, what would be the difference in population for the same time? Find it.​

Answer 1

To find the number of years it will take for the population of the colony to grow from 80,000 to 92,610 with a growth rate of 5% per annum, we can use the formula for compound interest:

Final Population = Initial Population * (1 + Growth Rate) ^ Number of Years

92,610 = 80,000 * (1 + 0.05) ^ t

Now, we can solve for t:

(92,610 / 80,000) = (1.05) ^ t

1.157625 = (1.05) ^ t

To find t, we can use logarithms:

t = log(1.157625) / log(1.05)

t ≈ 2.967

So, it will take approximately 2.967 years for the population to grow from 80,000 to 92,610 at a 5% growth rate.

Now, let's consider a 2% lower growth rate (5% - 2% = 3%). We can use the same formula to find the final population after the same time (2.967 years):

Final Population = Initial Population * (1 + Growth Rate) ^ Number of Years

Final Population = 80,000 * (1 + 0.03) ^ 2.967

Final Population ≈ 80,000 * 1.09364

Final Population ≈ 87,491.2

To find the difference in population for the same time, we can subtract the population with the lower growth rate from the population with the higher growth rate:

Difference in population = 92,610 - 87,491.2

Difference in population ≈ 5,118.8

So, the difference in population for the same time with a 2% lower growth rate would be approximately 5,118.8.