Question

Contagious diseases can spread very quickly. Suppose five people are ill during the first week of an epidemic and that each person who is ill spreads the disease to four people by the end of the next week. By the end of the tenth week of the epidemic, how many people have been affected by the illness?

Answer 1

Well, let's take it one week at a time. How many will be sick at the end of week 1?

Answer 2

ok theres 5 people ill in each spreads to 4 so 4*5=20 plus the 5=25

Answer 3

Good =) Keep goin'
Week 2

Answer 4

25 * 10=250 people in 10 weeks right

Answer 5

think of it as exponential function, with time in terms of weeks
you need initial value when t=0
you need to know the scale factor...after each week the amount multiplies by a constant each time

Answer 6

Nono, it doesn't go like that.

Answer 7

Dumbcow, I'm getting there =) Pattern recognition.

Answer 8

Week 0: 5 people
Week 1: 25 people
Week 2?

Answer 9

sorry..i like to jump ahead to formula, then fill in the missing pieces

Answer 10

I don't like to just hand a student a formula without making it mean something to them first.

Answer 11

ok so 25 *4

Answer 12

Brenda, you correctly said that after a week there would be 25 sick people. Now, in a weeks time, each of those 25 people will spread the disease to 4 new people.

Answer 13

Good =) 25*4, but then we keep that same 25, so it's
25*4 + 25
which is just 25*5

Answer 14

And I'd also point out that the first time, you did
5*4 + 5
which is just
5*5

Answer 15

ok so 25*4=100+25=125

Answer 16

so 125*4=500+125=625

Answer 17

Mhmm

Week 0: 5
Week 1: 25 (5*5)
Week 2: 125 (5*5*5)
Week 3: 625 (5*5*5*5)

Answer 18

625*4=2500+625=3125
3125*4=12500+3125=15625 right

Answer 19

You keep multiplying the number by 4 and then adding the number. I'd rather you just multiply by 5.

Answer 20

Do you see that it's the same?
n*4 + n = n*5

Answer 21

15625*4=62500+15625=78125
78125*4=312500+78125=390625

Answer 22

390625*4=1562500+390625=1953125

Answer 23

are u sure this is right numbers are too big

Answer 24

Okay, Brenda, what you're doing is right, and it's going to get you there.
But there's an easier way, especially with the problems that do more than 10 weeks.

Answer 25

And I'm sure it's right. The point is that it is very big numbers. It's called exponential growth.

Answer 26

But let's slow down and see if we can notice the pattern. First, can you agree that instead of multiplying the number by 4 and then adding the number, we can just multiply by 5?

Like for week 1, we start with 5 people.
You did
5*4 + 5 = 25
Couldn't you just have done
5*5 = 25

Answer 27

so what will be the answer 48828125

Answer 28

If I tell you that's the correct answer, are you going to leave and not let me teach you the easy way to do this kind of problem?

Answer 29

no im not

Answer 30

Your answer is correct =)

Answer 31

bye im leaving lol im just playing

Answer 32

Okay, now here's the key to this kind of problem.
Notice that there's a pattern to how the number of people is growing. What is the pattern?

Week 0: 5
Week 1: 25
Week 2: 125
Week 3: 625

What is the pattern? How do I get from one week to the next?

Answer 33

It might not be that obvious to you, but it multiplies by 5 every time.

Answer 34

*5

Answer 35

it mark my answer wrong are u sure thats it

Answer 36

Right. And there's a whole family of functions that work exactly like that. To get to the next number, you multiply by something each time.
It might double every time. It might triple every time. It might multiply by 10 every time.
Or it could be getting smaller
It could halve every time. It could be a third of the size each time. It might be one tenth every time.

Answer 37

I think it only marked you wrong because of a misunderstanding of how the problem was written. I think you did one extra week.

Answer 38

can u check

Answer 39

Take your answer and divide by 5. That's what you should have put in, I believe.

Answer 40

9765625

Answer 41

Does it accept that?

Answer 42

no

Answer 43

Okay, so the wording of this problem is kind of... lame. And I think it confused us mostly about how many times this disease was multiplying.

Here's the important info:
five people are ill during the first week
each person who is ill spreads the disease to four people by the end of the next week

Week 1: 5
Week 2: 25
Week 3: 125
Week 4: 625
Week 5: 5^5
...
Week 10: 5^10 = 9765625

Answer 44

it marks it wrong

Answer 45

Lol, well then it's somehow a mis-communication of the problem.