A fair die is rolled five times. A 5 is considered success while all other outcomes are failures. Find the probability of 0 succ
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Answer:
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