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January 27, 2015

January 27, 2015

Posted by **Lindsey** on Sunday, March 27, 2011 at 2:38pm.

During a past epidemic, the number of infected people increased exponentially with time, or f (t) = ab^t , where f is the number of infected people at time t, in days. Suppose that at the onset of the epidemic (0 days) there are 30 people infected, and 6 days after the onset there are 300 people infected.

a) Specify the function f, that models this situation, by determining a and b.

b) Predict the number of people who will be infected at the end of 2 weeks using your answer to a.

c) According to this function, approximately when will the number of infected people reach 10,000? (Use logarithms to sove this part - a guess and check answer WILL NOT be accepted)

- Algebra 2 -
**Henry**, Monday, March 28, 2011 at 6:15pmF(t) = 30b^6 = 300,

30b^6 = 300,

Divide both sides by 30:

b^6 = 10,

Take log of both sides:

6log(b) = log10,

log(b) = log10 / 6,

log(b) = 1/6,

Exponential form:

10^(1/6) = b,

Or b = 10^(1/6).

F(t) = 30*10^(1/6)^t,

a. Eq: F(t) = 30*10^(t/6).

b. F(14)=30*10^(14/6) = 6463 Infected.

c. 30*10^(t/6) = 10000,

Divide both sides by 30:

10^(t/6) = 10000/30.

(t/6)log10 = log10000 - log30 = 2.5229.

(t/6)log10 = 2.5229.

Divide both sides by log10:

t/6 = 2.5229,

Multiply both sides by 6:

t = 6 * 2.5229 = 15.14 = approximately 15 Days.

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