Question 9: The number of people living on a remote island decreases by 9% every 10 years.
In 1950 there were 18000 living on the island.
Calculate how many less people will be living on the island in 2020.
Question 10: A car was bought for £20,000.
Its value depreciates by 31% each year for the first four years.
What is its values at the end of the four years?
Question 11: A tree is 80cm when planted.
Each year the height of the tree increases by 22%.
After how many complete years will the height of tree be at least 3m?
Question 12: The number of polar bears in a region is decreasing by 5% per year.
There are 3000 polar bears in the region in 2017.
What year will be the first year with less than 1000 polar bears in the
region?
Question 13: Michael has started working for a company on a salary of £15000.
Each year he will be given a 6% pay rise.
How many years will it take for Michael's salary to exceed £30000?
Question 14: The value of a car decreases by 7.2% each year.
When bought the car cost £6200.
How many years will it take the car to have a value less than £1000?
Question 15: A full water tank has sprung a leak.
4% of the water is lost every minute.
What percentage of water is left in the tank after twenty minutes?
Question 16: A fish tank, that is full of water, has sprung a leak.
12% of the water is lost every hour.
What percentage of the water is lost after three hours?

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

can you complete your sentence? i could !