Situation 1
In this case, we have a person that originally has 80 followers. After 1 year, if the number of followers triples, then the person will have - after one year:
80 * 3 = 240
After the second year:
80 * 3 * 3 = 240 * 3 = 720
After the third year:
80 * 3 * 3 * 3 = 720 * 3 = 2160
After the fourth year:
80 * 3 *3 *3 * 3 = 2160 * 3 = 6480
This is a case of an exponential function in which we have:
[tex]f(x)=80\cdot(3)^x\Rightarrow f(x)=80\cdot3^4=f(4)=6480[/tex]
Therefore, the corresponding option is:
[tex]80\cdot3\cdot3\cdot3\cdot3[/tex]
[Option A.]
Situation 2
In this situation, we already know that the tank contains 80 gallons of water, and is getting filled at a rate of 3 gallons per minute.
We can say that we have a situation here that we can model using a linear equation. The constant rate of 3 gallons per minute is the slope of a line, m = 3, and the number of gallons that the tank already has, 80 gallons, is the y-intercept of the line, b = 80.
If we remember that the slope-intercept form of the line is:
[tex]y=mx+b[/tex]
Then we have:
[tex]f(t)=3t+80[/tex]
Which represents the gallons the tank has as a function of minutes, t.
Then, after 4 minutes, we will have:
[tex]f(4)=3\cdot4+80=80+4\cdot3[/tex]
Therefore, the letter that corresponds to this situation is the letter D.
In summary, we can say that:
Situation 1 corresponds to the letter A ---> A. 80 * 3 * 3 * 3 *3.
Situation 2 corresponds to the letter D ---> D. 80 + 4 * 3.
