The train holds 66 passengers. It starts out empty.
It picks up 1 passenger at the first station, 2 passengers at the second station, 3
passengers at the third station, and so on.
No one gets off.
After how many stations will the train be full?

11 stations.

Step-by-step explanation:

1st stop = 1

2nd stop 1+2=3

3rd stop 3+3=6

4th stop 6+4=10

5th stop 10+5=15

6th stop 15+6=21

7th stop 21+7=28

8th stop 28+8=36

9th stop 36+9=45

10th stop 45+10=55

11th stop 55+11=66

As base of the exponential term 2 is greater than 1 so it will be exponential increasing graph as shown in attachment.

A.Statement 1 is incorrect because the y-values are increased by 2, not doubled.

Statement 1 was correct as value will be doubled with every increase in x.

We can check it this way

Like for

for (its double of 2)

for (its doubled of 4)

So statement 1 was correct

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B.Statement 2 is incorrect because the y-values are doubled, not halved.

This is also incorrect as statement 2 talks when x " decreases" then y will be halved

like you can check it this when

for

now when x is decreased from 3 to 2

then for (its half of 8)

so statement 2 was also correct

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C.The conclusion is incorrect because the range is limited to the set of integers.

This is also incorrect as we can have x as some non integer numbers like

for which is not integer

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D.The conclusion is incorrect because the range is limited to the set of positive real numbers.

This is correct as exponential terms will always be a positive number as you can see from graph in attachment, exponential curve will never cross x axis line or go below x axis, so it can never be negative. So range is all positrive real numbers

so choice (D) is the right answer