The population of a town double every 10 years from 1960 to 1990.what was the percent increase in population during this time
it doubled 3 times in the 30 years. So, it is now 8 times as great.
That is 800% as much as it started.
However, if you want the annual growth rate, that is 2^(1/10) = 1.07 or 7% per year
Well, if the population of the town doubled every 10 years from 1960 to 1990, I'd say the percent increase was purely exponential: "It doubled, it doubled again, it doubled some more, and then doubled one more time for good measure!" That's a lot of doubling! But let's get specific. If we take the starting population in 1960 as 100%, then we would have had another 100% increase in 1970, bringing us to 200%. Then another 100% increase in 1980, bringing us to 400%. And finally, another 100% increase in 1990, bringing us to a whopping 800%! So, the percent increase in population during this time was a hilarious 800%! That's what I call exponential growth on a level worthy of an endless clown car parade!
To find the percent increase in population during this time, we can use the formula:
Percent Increase = (Final Value - Initial Value) / Initial Value * 100
Let's calculate step-by-step:
Step 1: Determine the initial population in 1960.
Given that the population doubles every 10 years, the initial population in 1960 is half the population in 1970.
So, we need to find the population in 1970 and divide it by 2.
Assuming the population in 1970 is P, the initial population in 1960 is P/2.
Step 2: Calculate the final population in 1990.
Since the population doubles every 10 years, from 1960 to 1990, there are 3 sets of 10-year intervals.
So, the population in 1990 is 2^3 times the population in 1960.
Assuming the population in 1960 is P, the final population in 1990 is 2^3 * P = 8P.
Step 3: Calculate the percent increase using the formula.
Given that the initial population is P/2 and the final population is 8P, the percent increase is:
Percent Increase = (8P - P/2) / (P/2) * 100
= (16P - P) / (P/2) * 100
= (15P) / (P/2) * 100
= 15 * 2 * 100
= 3000
Therefore, the percent increase in population during this time is 3000%.
To find the percent increase in population during this time period, you'll need to calculate the population growth rate. Here's how you can do it:
1. Determine the number of times the population doubled over the given time period. In this case, the time period is from 1960 to 1990, which is 30 years. Since the population doubles every 10 years, the population doubled 30/10 = 3 times.
2. Calculate the overall population growth rate using the formula: growth rate = (final population / initial population)^(1/number of periods) - 1.
To fill in the formula:
- The final population is 2 times the initial population, since it doubled three times: final population = 2^3 = 8.
- The initial population is 1.
- The number of periods is 3, as mentioned earlier.
3. Plug in the values and calculate the growth rate: growth rate = (8/1)^(1/3) - 1 = 2 - 1 = 1.
4. Convert the growth rate to a percentage by multiplying it by 100: growth in percentage = 1 * 100 = 100%.
Therefore, the percent increase in population during this time period is 100%.