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2 answers:
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72 
1÷9 = 111.... 2÷9 = 222.... and so on.
The proof is a little more difficult.
Think of all those repeating ones as a variable - let's call it n
so n= .111111......... repeating
How can we get a single one of those ones to jump across the decimal and be on the left side. We can multiply all of those ones by 10.
10n (ten times the original number) = 1.1111111 (ones still go on forever)
Now here is the interesting part. Let's take all the repeating ones in the first number we made away from the second number.
10n = 1. 1111111......
<u>- n = . 1111111....
</u>9n = 1 (all of the repeaters are gone and only the one we moved to the left
of the decimal is left)
Now let's divide by 9 to get n by itself
<u>9n</u> = <u>1
</u>9 9
And voila! n = 1/9
So to repeat 72.111... written as a fraction is 72
The proof is a little more difficult.
Think of all those repeating ones as a variable - let's call it n
so n= .111111......... repeating
How can we get a single one of those ones to jump across the decimal and be on the left side. We can multiply all of those ones by 10.
10n (ten times the original number) = 1.1111111 (ones still go on forever)
Now here is the interesting part. Let's take all the repeating ones in the first number we made away from the second number.
10n = 1. 1111111......
<u>- n = . 1111111....
</u>9n = 1 (all of the repeaters are gone and only the one we moved to the left
of the decimal is left)
Now let's divide by 9 to get n by itself
<u>9n</u> = <u>1
</u>9 9
And voila! n = 1/9
So to repeat 72.111... written as a fraction is 72
There were 2.07 times as much people that applied in the fourth month than in the first month.
<h3>What is an exponential function?</h3>An exponential function is one that grows or decreases in an exponential manner. Thus, for any exponential function we can write; f(x) = ax^±n. The term a is the initial value x is the rate of change while n is the time elapsed. The positive sign is used for an exponential increase while the negative sign is used for an exponential decrease.
Thus we have;
f(x) = 27(1.2)^4
This shows us that the time elapsed is four months and f(x) = 2.07.
Therefore, there were 2.07 times as much people that applied in the fourth month than in the first month.
Learn more about exponential function:brainly.com/question/11487261?
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