I have no idea how to even start this problem.
In 1951, the population of India was 357 million people. By 1981 it had grown to 984 million. If the population is growing exponentially, when (in what month of what year) will the population reach 1 billion people?
To solve this problem, you need to understand the concept of exponential growth and use it to find the time when the population reaches 1 billion people.
Here's how you can approach the problem step-by-step:
Step 1: Determine the growth rate
First, calculate the growth rate using the given data. The growth rate can be found by dividing the final population by the initial population and taking the nth root, where n represents the number of years between the two populations.
In this case, the growth rate is given by:
G = (Final population / Initial population)^(1/n)
Where Final population = 984 million, Initial population = 357 million, and n = number of years = 1981 - 1951 = 30.
G = (984/357)^(1/30)
Step 2: Calculate the growth factor
Next, compute the growth factor by adding 1 to the growth rate calculated in step 1:
Growth factor = G + 1
Step 3: Determine the time it takes to reach 1 billion people
To find the time it takes for the population to reach 1 billion people, solve for time using the exponential growth formula:
Final population = Initial population * (Growth factor)^time
In this case, the final population is 1 billion and the initial population is 357 million. You need to solve for time.
1 billion = 357 million * (Growth factor)^time
Step 4: Solve for time
Rearrange the equation and solve for time:
(Growth factor)^time = (Final population / Initial population)
Take the logarithm of both sides to solve for time:
log(Growth factor)^time = log(Final population / Initial population)
time * log(Growth factor) = log(Final population / Initial population)
time = log(Final population / Initial population) / log(Growth factor)
Substitute the values into the equation and solve for time.
Step 5: Convert time to months and years
Lastly, once you have obtained the time in years, you can convert it to months and years. Multiply the decimal part of the year by 12 to get the number of months. The whole part of the year will give you the year.
For example, if the calculated time is 2.5 years, it would be 2 years and 6 months.
By following these steps, you should be able to determine the month and year when India's population will reach 1 billion people.