The population of a city in 2005 was 18,000. By 2010, the city’s population had grown to 45,000. Economists have determined that the population growth follows an exponential model. If they are correct, what is the projected population for 2015?
The answer is 47600
To determine the projected population for 2015 using an exponential model, we need to find the growth rate and use it to forecast the population.
Step 1: Find the growth rate (r)
To find the growth rate, we will use the formula:
r = (P2/P1)^(1/t) - 1,
where P1 is the initial population, P2 is the final population, and t is the time between the two populations.
Given:
P1 = 18,000 (initial population in 2005)
P2 = 45,000 (final population in 2010)
t = 5 years (from 2005 to 2010)
Using the formula, we can calculate the growth rate:
r = (45,000/18,000)^(1/5) - 1
r = 2.5^(1/5) - 1
r ≈ 0.379729661461
Step 2: Forecast the population for 2015
Now that we have the growth rate, we can forecast the population for 2015. Since the population at the end of 2010 is our new initial population, we can use the formula:
P = P1 * (1 + r)^t,
where P is the projected population, P1 is the initial population, r is the growth rate, and t is the time between the initial population and the projected population.
Given:
P1 = 45,000 (population in 2010)
t = 5 years (from 2010 to 2015)
r ≈ 0.379729661461 (growth rate)
Using the formula, we can calculate the projected population for 2015:
P = 45,000 * (1 + 0.379729661461)^5
P ≈ 45,000 * 1.85772236894
P ≈ 83,598.505
Therefore, the projected population for 2015 is approximately 83,598.
45/18 = 5/2
it grew by that factor in 5 years.
So, in the next 5 years it will grow by another factor of 5/2 to 45,000 * 5/2
Answer is 12500
The Answer I got was 72000
2005 to 2010 is 5 years, and 2010 to 2015 is 5 years. The way to solve it would be to find out how much growth there was from 2005 to 2010, and apply that same principle here.
So 45000-18000 = 27,000
Since the growth is linear, we can say that 27,000+45,000 would be the equation to solve this question.
(72,000 is my answer)
why "oh well"?
45,000 * 5/2 = 112500
it was 112500 I think
oh well