Write an equation for the graph below in terms of x
1 answer:
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1) See attachment.
2) See attachment
3)
4) 17.8 days
Step-by-step explanation:
1)
The table is in attachment.
In this problem, we are told that the initial number of people infected ad day zero is two, so the first row is (0,2).
Then, we are told that each day, an infected person infects 2 additional people. Therefore, at day 1, the number of infected people will be 2*2=4.
Then, each of the 4 persons infect 2 additional persons, so the number of infected people at day 2 will be 4*2=8.
Continuing the sequence, the following days the number of infected people will be:
8*2 = 16
16*2 = 32
32*2 = 64
2)
The graph representing the situation is shown in attachment.
On the x-axis, we have represented the day, from zero to 5.
On the y-axis, we have represented the number of infected people.
We see that the points on the graph are:
0, 2
1, 4
2, 8
3, 16
4, 32
5, 64
3)
Here we have to create a mathematics model (so, an equation) representing this scenario.
First of all, we notice that the number of infected people at day 0 is 2:
To write an equation, we call the number of the day; this means that at x = 0, the value of y (number of infected people) is 2:
Then, at day 1 (x=1), the number of infected people is doubled:
And so on. This means that for each increase of x of 1 unit, the value of y doubles: so, we can represents the model as
Or
4)
Here we are told that the entire city has a population of
p = 450,000
people.
In order for the virus to infect the whole population, it means that the value of y must be equal to the total population:
y = 450,000
Substituting into the equation of the model, this means that
And solving for x, we find the number of days after which this will happen:
So, after 17.8 days.
