E. What was the population in 1995? (the initial population for this situation) *
491147
98
501170
481890
f. What is the growth/decay factor? ( = 1 +/- rate of population change) *
.98
1.02
-.20
-.02
g. Is the population increasing or decreasing? *
Increasing
Decreasing
Task 3
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.
h. Write an exponential function to represent the town's population, y, based on the number of years that pass, x after 1995. *
y = 1.11x + 1995
y = 25400(1 + .11)^x
y = 25400 + 1.11x
y = 1995 (1.11)^x
i. Based on the function, what is the population predicted to be in the year 2020? *
204783
345071
535686
704850

Part e)

Part f) The decay factor is 0.98

Part g) Decreasing

Part h)

Part i)

Step-by-step explanation:

we have

where

x ----> is the number of years since 1995

f(x) ----> is the population of a Texas city

Part e) What was the population in 1995?

we know that

The equation of a exponential function decay is of the form

where

a represent the initial value (y-intercept of the function)

therefore

In the given function

The initial value is the value of the function when the value of x is equal to zero

so

For x=0

Part f) What is the growth/decay factor?

we know that

The equation of a exponential decay function is of the form

where

(1-r) ----> is the decay factor

In this problem we have

(1-r)=0.98

therefore

The decay factor is 0.98

Part g) Is the population increasing or decreasing?

we know that

If the factor is greater than 1 then the population is increasing

If the factor is less than 1 and greater than zero, then the population is decreasing

In this problem

the factor is less than 1

0.98< 1 ----> is a decay factor

therefore

The population is decreasing

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

Part h) Write an exponential function to represent the town's population, y, based on the number of years that pass, x after 1995

we know that

The equation of a exponential growth function is of the form

we have

substitute

Part i) Based on the function, what is the population predicted to be in the year 2020?

Remember that the number of years is since 1995

so

x=2020-1995=25 years

substitute the value of x in the exponential function

the answer is 5636.7