Question

(40 POINTS)

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.
1. Write an exponential function to represent the town's population, y, based on the number of years that passed, x, after 1995
2. When will the town surpass 302438?

Answer 1

Explanation:

Answer 2

1. y= 25400(1 + 0.11)^x

2. 2019

Explanation:

1. y = a(1 + r)^x

(exponential growth formula :

a = initial value (the amount before measuring growth or decay)

r = growth or decay rate (usually represented as a percentage and expressed as a decimal)

x = number of time units that have passed)

y= 25400(1 + 0.11)^x

so in 1 year, in 1996, we would say

y=25400(1+0.11)^1

y=25400(1.11)

y=28194

2. I found the answer by plugging in numbers into x

with x = 24

y= 25400(1+0.11)^24

y= 310874

so in 24 years, the population will surpass 302438 which would be 1995+24= 2019