Answer only IF your SURE?

Question

On January 8, 10 students come down with the flu. Assume that each day, the number of students who come down with the flu doubles. So, for example,20 students come down with the flu january 9th. Let f(t) repersent the number of students who come down with the flu at t days since January 8.

1 Find an equation for t
2 Find f(7).What does your result mean in terms of the situation.

Answer 1

The previous answers are almost correct, but it's not that 1280 students have the flu after one week, it's that on the seventh day, 1280 students come down with the flu. How many students have the flu at that time depends on how many have already recovered, but it's potentially as many as 2550

Answer 2

When t = 1, 20 students come down with the flu, leaving a total of 30 students sick, so we need a term that varies with t, doubling each time t increases by 1. An exponential is the way to go.

f(t) = 10*2^t

When t = 0, it is January 8th, and we have 10*2^0 = 10*1 = 10 students getting sick.
When t = 1, it is January 9th, and we have 10*2^1 = 10*2 = 20 students getting sick.
When t = 2, it is January 10th, and we have 10*2^2 = 10*4 = 40 students getting sick.

This equation fits the pattern.

f(7) means t = 7, so the number of students that get sick on the 7th day is
10*2^7 = 10*128 = 1280 students

Answer 3

1. The equation is f(x)=10(2^t) as has already been explained by others.
2. f(7)= 1280 were sick on that day but the questions seems to be asking for the total number since Jan 8. You would need to represent this as a finite series with the upper limit of t being 7 and the lower being 0 (Jan 8 is day 0), and the equation to be seried is 10(2^t). Thus the answer would look like this :
10(2^7) + 10(2^6) + 10(2^5) + 10(2^4) + 10(2^3) + 10(2^2) + 10(2^1) + 10(2^0) which is 2550 total students ill

Answer 4

1) Doubling will look like 2^t, but we need to adjust for initial conditions. When t = 0, 2^t = 2^0 = 1.
Thus try 10 * 2^t.
When t=0, we have our initial 10 students
When t=1, we have 10*2 = 20, which is double.
so it works!
2) f(7) will be the number of students who come down with the flu 7 days after Jan 8th (which would be Jan 15th). So 10 * 2^7 = 1280 students will come down with the flu.
Eeks - time to cancel school!

Answer 5

f(t) = 10*2^t
f(7) = 10*2^7= 1280 additional students got the flu 7 days after January 8.

The total number of students with the flu 7days after January 8 is 10*(1-2^8)/(1-2) = 2550

Answer 6

let t = 0 be the time on Jan 8th, there are 10 students who has flue

the next day, Jan 9th, t = 1, 20 students how has flu

(0,10) and (1,20)

doubles everyday means this is an exponential function

y = ab^2

10 = ab^0
20 = ab^1

10 = ab^0
10 = a * 1
a = 10

20 = 10 (b)^1
2 = b^1
b = 2

the equation is:

f(t) = 10(2)^t

Jan 7th is the day before Jan 8th on which t = 0. That means t = -1 on Jan 7th

f(-1) = 10(2)^-1
f(-1) = 10 * 1/2
f(-1) = 5 students who has flues

P.S. if you meant the number 7 is 7 days after Jan 8, then:

f(7) = 10(2)^7
f(7) = 1280 students who has flu

Answer 7

f(t) = 10(2^(t-1))
why t-1? Because on day 1 is the 8th january (f(1) = 10)

f(7) = 10(2^6)
= 640
it means that on day 7(14th of january), 640 students had flu.

Answer 8

1.) f(t) = 10 * (2)^t
2.) f(7) = 10 * 2^7 = 10 * 128 = 1280. This means that after a week, 1280 students had the flu.

Answer 9

5*2^t is the equation if you call t=1 January 8.
10*2^t is the equation if you call t=0 January 8.
5*2^7=5*128=640
10*2^t=10*128=1280

Answer 10

(1) f(t) = 10(2^t)

(2) f(7) = 1,280

1280 students have the flu after one week.