Question

1:The first time a census was taken in Esinville, the population was 12,621. Each year after that, the population was about 6% higher than it was the previous year.

Sketch the graph that represents the situation. Let x represent the number of years since the first census was taken.

What are the coordinates of the point that contains the ­y-intercept?



(0, 12,621)

(12,621, 0)

(1, 12,621)

(12,621, 1)
2:Doug buys a pint of strawberries every week. The first time he bought them, they cost $2.60. He notices the price is getting more expensive, at a rate of 7% per week.

Doug sketches a graph of the situation.

Which statements are true?

Select each correct answer.



The graph decreases from left to right.

The point ​ (0, 2.60) ​is on the graph.

The graph has a y-intercept only.

The graph has an x-intercept and a y-intercept.

The point (2.60, 0) is on the graph.

The graph increases from left to right.
3:A scientist performed an experiment with a radioactive substance whose half-life is 22 min. The scientist will sketch a graph of the situation, where x represents the time since the scientist first measured the substance, and y represents the amount of radioactive substance remaining at that time.
The scientist will only sketch the graph in the quadrant or quadrants for which it makes sense to.

In which quadrant or quadrants will the scientist sketch the graph?



Quadrants I, II, III, and IV

Quadrants I and II only

Quadrant I only

Quadrants I and IV only
4:The graph represents the atmospheric pressure, in ounces per square centimeter, as a function of altitude in kilometers above sea level.

Which statements accurately reflect this relationship?

Select each correct answer.



The atmospheric pressure gets close to 36 oz/cm2 as the altitude continues to increase.

The atmospheric pressure is 0 oz/cm2 at sea level.

As the altitude continues to increase, the atmospheric pressure approaches 0 oz/cm2 .

As the altitude decreases, the atmospheric pressure increases.
5:The graph shows the total monthly sales as a function of the number of cake tiers.

Which statement is true?



As the number of cake tiers increases without bound, the total monthly sales increase without bound.

As the number of cake tiers decreases, the total monthly sales increase without bound.

As the number of cake tiers increases without bound, the total monthly sales decrease without bound.

There is no limit to the number of cake tiers, but there is a limit to the total monthly sales.

Answer 1

Part 1:

The y-intercept is the value of y when x is zero. It is the initial value of a function represented by a graph.

Given that the first time a census was taken in Esinville, the population was 12,621, then the coordinates of the point that contains the ­y-intercept is (0, 12621)



Part 2:

Given that he notices the price is getting more expensive, at a rate of 7% per week (i.e. the graph increases from left to right).
Thus, the graph does not decrease from left to right but increases from left to right.

Given that the first time he bought them, they cost $2.60, thus point (0, 2.60) is on the graph.

From the graph it can be seen that the graph crosses the x axis at a negative value of x, thus point (2.6, 0) in not on the graph; the graph have only a y axis (since it is not possible to have a negative number of biscuit).

Therefore, the statements that are true are:

The point ​ (0, 2.60) ​is on the graph.

The graph has a y-intercept only.

The graph increases from left to right.



Part 3:

The amount of subtance left of a radioactive substance after a time of t seconds is given by:

$N(t)=N_0e^{-kt}$

where t ≥ 0.

Therefore, the graph is in the positive x-axis and because exponential function always results in a postive number the graph is also in the positive y-axis.

Since the graph is in the positive x-axis (i.e. x is positive) and the graph is also in the positive y-axis (i.e. y is positive), the graph is in the 1st quadrant.

Therefore, the quadrant in which the scientist will sketch the graph is in quadrant 1 only.



Part 4:

From the given graph it an be seen that as the altitude continues to increase, the atmospheric pressure approaches 0 oz/cm^2.

It can also be seen that as the altitude decreases, the atmospheric pressure increases.

Therefore, the statements accurately reflect this relationship are:

As the altitude continues to increase, the atmospheric pressure approaches 0 oz/cm2 .

As the altitude decreases, the atmospheric pressure increases.



Part 5:

From the graph it can be seen that as the number of cake tiers increases without bound, the total monthly sales increase without bound.

Therefore, the true statement is:

As the number of cake tiers increases without bound, the total monthly sales increase without bound.

Answer 2

Answer:

For detailed answer read the description below.

Step-by-step explanation:

1. Given information

   Total population was 12621

   So, next year population

 $=12621*(106/100)\\=13380$

For the next year the population will be

 $=13380*(160/100)\\=14183$  

For next year the population will be

$=14183*(106/100)\\=15034$

Now , on plotting the above data on the graph

we get, the coordinates of the point that contains y - intercept is (0 ,12621).

2. Given information

The first time he bought at a cost of $2.60

Price getting more expensive per week = 7%

So, price for the next order will be

$= 2.60+(0.07*2.60)\\=2.782$

Similarly, for the next time price will be 2.976 and 3.184 respectively.

On plotting the above information on graph one can see that the graph has only a y-axis hence it is not possible to get a negative value from the graph.

Hence, the correct options are:

(1) the point (0 , 2.60) is on the graph.

(2) The graph has a y- intercept only.

(3)The graph increases from left to right.

3. Given information :

The scientist perform experiment with a radioactive substance

Half life of substance = $22 min.$

As, we know that the expression for the half life is given as :

$A(t) = A_0(1/2)^\frac{t}{T}$

where, $t$ is time period and $A$ is amount of substance left.

As, it is clear from the expression that graph will exponentially decrease but it will never b negative.

Hence, The graph will be in 1st quadrant only.

4. Given information:

The atmospheric pressure in ounces per square cm.

And, it is function of altitude above sea level

As we know that the expression for the pressure is written as:

$p=C . e^(\frac{-Mgh}{RT})$

If we plot the graph of the above equation by putting the values we get

from the expression that graph will exponentially decrease.

It is also can be seen that as altitude decreases , the atmospheric pressure increases.

Hence the correct options are:

(1) As the altitude continuous to increase ,  the atmospheric pressure approaches to $0 oz/cm^2$

(2) As the altitude decreases , the atmospheric pressure increases.

5. Given information

Total monthly sales as a function of the number of cake tiers.

Now, from the graph one can conclude that as the number of cake tiers increases , the total monthly sales increases without bound.

Hence the true statement is:

As the number of cake tiers increases without bond , the total monthly sales increase without bond.

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