the population of the city in 2005 was 18,000 by 2010 the city's population had grown to 45,000. Economics have determined that the population follows an exponential model. If they are correct what is the projected population for 2015
To find the exponential equation, we can use the formula:
y = a(1 + r)^t
Where:
y = population
a = initial population (18,000)
r = growth rate (unknown)
t = time (in years)
We can use the information given to find r:
45,000 = 18,000(1 + r)^5
Dividing both sides by 18,000:
2.5 = (1 + r)^5
Taking the 5th root of both sides:
1.169 = 1 + r
r = 0.169
Now we can use this growth rate to find the population in 2015:
y = 18,000(1 + 0.169)^10
y = 18,000(3.118)
y = 56,124
Therefore, the projected population for 2015 is approximately 56,124.