On the first day of college, Sophia tells a rumor to three of her friends. Each of those friends tells the rumor to three of their friends the next day. Each person who hears the rumor on the second day shares it with three more people on the third day, and so on. So, every day, the number of people who hear the rumor is three times the number who heard it on the previous day. Determine the number of people who hear the rumor on the sixth day.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

m=-16

step-by-step explanation: