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# Math Help please!!! :)?

The number of students infected with flu at a school after t days is modeled by the function

p(t) = 600 / (1 + 19e^(-0.3t))

1. what was the initial number of students infected?

2. The school will close when 500 of the 600 students are infected. After how many days will it close?

Thanks in advance :)

### 2 Answers

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For Question # 1 set 't' equal to zero and solve for p(t)

hint: find p(0)

For question # 2 find the time 't' when p(t) = 500

so set p(t) = 500

500 = 600 / (1 + 19e^(-0.3t))

500 + 9500e^-0.3t = 600

9500e^-0.3t = 100

e^-0.3t = 100 / 9500

take the natural log of both sides to get

-0.3t = ln(100/9500)

0.3t = - ln(100/9500)

t = 15.18

So after 15.18 days the school will close.

• 1) p(0) = 600/[1+19] = 30 students

2) 500 = 600 / (1 + 19e^(-0.3t))

1 + 19e^(-0.3t) = 600/500 = 1.2

e^(-0.3t) = 0.2/19

-0.3t = ln(0.2/19)

t = 15.18 days

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