Question

An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, P, who contracted the flu t days after it broke out is given by the model P = − t ² + 13t + 130, where 1 ≤ t ≤ 6. Find the day that 160 students had the flu. Recall that the restriction on t is at most 6.

Answer 1

Answer:

At the 3rd day 160 students caught flu.

Step-by-step explanation:

Consider the provided model P = − t ² + 13t + 130 where 1 ≤ t ≤ 6

The total number of students is represents by P.

We need to find the day that 160 students had the flu.

Substitute the value of P=160 in above formula.

$160 = -t^2 + 13t + 130$

$160+t^2 - 13t - 130=0$

$t^2 - 13t +30=0$

$t^2 - 10t-3t +30=0$

$t(t-10)-3(t-10)=0$

$(t-10)(t-3)=0$

Hence the value of t=10 or t=3

But it is given that  1 ≤ t ≤ 6, Therefore select t=3

Hence, at the 3rd day 160 students caught flu.

Answer 2

At the 3rd day 160 students caught flu.

Calculation of the number of days:

Since  P = − t ² + 13t + 130, where 1 ≤ t ≤ 6.

So,

$160 = - t^2 + 13t + 130\\\\160 + t^2 -13t - 130 = 0\\\\t^2 -13t - 130= 0\\\\t^2 - 10t - 3t - 130 = 0\\\\t(t - 10) - 3(t - 10) = 0\\\\(t - 10) (t - 3) = 0$

Therefore,  the value of t=10 or t=3

Since  1 ≤ t ≤ 6, So here we select

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