The population of a country increases at the rate of 3% per annum. How many years will it take to double itself?
S = 2p
P(1+r)^n = 2p
(1+r)^n = 2
1.03^n = 2
taking log both sides we get
n log (1.03) = log2
Simpltying
n = 23.45
S = 2p
P(1+r)^n = 2p
(1+r)^n = 2
1.03^n = 2
taking log both sides we get
n log (1.03) = log2
Simpliying
n = 23.45
To find out how many years it will take for the population to double, we can use the formula for compound interest:
A = P * (1 + r/100)^t
Where:
A = Final amount (double the initial population)
P = Initial amount (starting population)
r = Rate of increase (in this case, 3%)
t = Time (in years)
In this case, we want to find the value of t when A = 2P:
2P = P * (1 + 3/100)^t
Divide both sides by P:
2 = (1 + 3/100)^t
Taking the logarithm of both sides:
log(2) = log((1 + 3/100)^t)
Using the property of logarithms:
log(2) = t * log(1 + 3/100)
Rearranging the equation:
t = log(2) / log(1 + 3/100)
Using a calculator, we can find the value of t:
t ≈ 23.45 years
Therefore, it will take approximately 23.45 years for the population to double itself.
To find out how many years it will take for the population of a country to double itself, we can use the concept of exponential growth.
The formula for exponential growth is given by:
P = P0 * (1 + r/100)^t
Where:
P = Final population
P0 = Initial population
r = Growth rate per year
t = Number of years
In this case, the initial population is P0, the growth rate is 3%, and we want to find out the number of years (t) it takes for the population to double (P = 2 * P0).
Substituting these values into the formula, we have:
2 * P0 = P0 * (1 + 3/100)^t
Simplifying the equation, we get:
2 = (1.03)^t
Now, to solve for t, we can take the logarithm of both sides of the equation:
log(2) = log((1.03)^t)
Using the logarithmic identity that log(a^b) = b * log(a), we can rewrite the equation as:
log(2) = t * log(1.03)
Finally, we can solve for t by dividing both sides of the equation by log(1.03):
t = log(2) / log(1.03)
Using a calculator, we can evaluate this expression to find the value of t.
Therefore, by using the formula for exponential growth and solving for the unknown variable, we can determine the number of years it will take for the population of a country to double itself.