In the year 1995, the population of a town in Texas was recorded as 25,400 people. Each year since 1995, the population has increased on average by 11% each year.
8. Based on the function, what is the population predicted to be in the year 2020?
(Round up the nearest person--no decimals).
1995 ----> t = 0
2020 ---- t = 25
pop. = 25400(1.11)^25
= 345,071
(ambitious town)
mathhelper is correct
To calculate the population in the year 2020, we can use the formula:
P(t) = P0 * (1 + r)^t
Where:
- P(t) is the population at time t
- P0 is the initial population (25,400 people in 1995)
- r is the average annual growth rate (11%)
- t is the number of years since 1995 (2020 - 1995 = 25 years)
Plugging in the values:
P(t) = 25,400 * (1 + 0.11)^25
Calculating this equation gives us:
P(t) = 25,400 * (1.11)^25 ā 115,824
So, the population predicted to be in the year 2020 is approximately 115,824 people (rounded up to the nearest person).
To find the population predicted to be in the year 2020, we can use exponential growth formula:
P = P0 * (1 + r)^t
Where:
P = population after time t
P0 = initial population (in 1995)
r = growth rate (11% or 0.11 as a decimal)
t = number of years since the initial year (2020 - 1995 = 25)
Let's substitute the values into the formula:
P = 25,400 * (1 + 0.11)^25
Now, we can calculate the population predicted to be in the year 2020:
P = 25,400 * (1.11)^25
Calculating this equation gives us the following result:
P ā 97,385
Therefore, the population predicted to be in the year 2020 is approximately 97,385 people.