SOLUTION: The population of a city grows exponentially according to the following relation: P= 5000(1.015)^t, where P is the estimated population and t is the number of years after 2005.

Algebra ->  Exponents -> SOLUTION: The population of a city grows exponentially according to the following relation: P= 5000(1.015)^t, where P is the estimated population and t is the number of years after 2005.       Log On


   

Question 1196942: The population of a city grows exponentially according to the following relation: P= 5000(1.015)^t, where P is the estimated population and t is the number of years after 2005.
What was the population in 2005?
What will be the population in 2028?

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Plug in t = 0 since we are at the point 0 years after 2005
P = 5000*(1.015)^t
P = 5000*(1.015)^0
P = 5000*(1)
P = 5000

A shortcut is to note that P = a*b^t has 'a' as the initial value.

Question: What was the population in 2005?
Answer: 5000

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2028 - 2005 = 23
23 years have elapsed from 2005 to 2028
We'll plug this in for the variable t.
P = 5000*(1.015)^t
P = 5000*(1.015)^28
P = 5000*1.5172221800974
P = 7586.110900487
P = 7586
We round to the nearest whole number since we can't have 0.1109 of a person

Question: What will be the population in 2028?
Answer: 7586