Question

The function

describes the spread of a rumor among a group of people in an enclosed space. N represents the number of people who have heard the rumor, and t is measured in minutes since the rumor was started. Which of the following statements are true? Check all that apply.

A. There are 300 people in the enclosed space.
B. It will take 30 minutes for 100 people to hear the rumor.
C. The rate at which the rumor spreads speeds up over time.
D. Initially, one person had heard the rumor.

Answer 1

Let's check the first one, if we set \[t \rightarrow \infty\], then
\[N(\infty) =\frac{ 300 }{ 1+0 } = 300\]
So, statement A is True

Answer 2

And I believe D is also correct?

Answer 3

if se plug t = 30 in the formula we get:
\[N(30) = \frac{ 300 }{ 1+299e^{-0.36\times 30} } = 298.18 \approx 298\]

Answer 4

B is False

Answer 5

Yes, D is true because if we plug t = 0, we get N(0) = 1

Answer 6

Now the C statement tells us about rate of change, so we need to take the first derivative os this formula and check if the function increases with time

Answer 7

you know how to take this derivative?

Answer 8

No

Answer 9

I don't think it changes at least not until it reaches 300

Answer 10

Think about it, if only one person knows the rumor, the speed of propagation of the rumor is not that big, but when many people knows about the rumor, the rumor will spread faster, right?

Answer 11

we have the equation that tells us the number of people that knows the rumor, if we want to know the rate of change, or in this case the speed that the rumor spreads, we need to take the derivative of this equation

Answer 12

and then analyse this new equation, i.e. if this equation in growing with time

Answer 13

So then it does change?

Answer 14

initially, yes, but then it decreases

Answer 15

So C would be correct?

Answer 16

it's not completely true, so i guess it's not true

Answer 17

Ah so A and D only?

Answer 18

Thank you

Answer 19

:)

Answer 20

What can you say about the continuous function that generated the following table of values?

A. the function has exactly one x-intercept
B. the function has more than one x-intercept
C. not enough information to answer the question
D. the function has no x-intercepts

Answer 21

B