Application of Exponential Functions

Real-World Problem:

1. The population of a city is P = 250,342e^0.012t where t = 0 represents the population in the year 2000.
2. Find the population of the city in the year 2010.

To find the population in the year 2010, we need to let t = 10 in our given equation.

P = 250,342e^0.012(10) = 250,342e^0.12 = 282,259.82

Since we are dealing with the population of a city, we normally round to a whole number, in this case 282,260 people.

1. Find the population of the city in the year 2015.

To find the population in the year 2015, we need to let t = 15.

P = 250,342e^0.012(15) = 250,342e^0.18 = 299,713.8

We’ll round this answer to 299,714 people.

1. Find when the population will be 320,000.
2. 320,000 = 250,342e^0.012(t)

SAT Prep:

• Example: A population increase of 4.5 percent per year.

b = 100% + 4.5% = 104.5% = 1.045

• Example: A population decrease of 3 percent per year.

b = 100% – 3% = 97% = 0.97