the number of people in a small town who are reached by a rumor about the mayor and an intern is given by n…

the number of people in a small town who are reached by a rumor about the mayor and an intern is given by n = 10,000 / (1 + 100e^(-0.8t)), where t is the number of days after the rumor begins. complete parts (a)-(c). a) how many people will have heard the rumor by the end of the first day? (round to the nearest integer as needed.)

the number of people in a small town who are reached by a rumor about the mayor and an intern is given by n = 10,000 / (1 + 100e^(-0.8t)), where t is the number of days after the rumor begins. complete parts (a)-(c). a) how many people will have heard the rumor by the end of the first day? (round to the nearest integer as needed.)

Answer

Explanation:

Step1: Substitute t = 1 into the formula

We are given $N=\frac{10000}{1 + 100e^{-0.8t}}$, substituting $t = 1$ gives $N=\frac{10000}{1+100e^{-0.8\times1}}$.

Step2: Calculate the value of $e^{- 0.8}$

We know that $e^{-0.8}\approx0.4493$. Then $100e^{-0.8}=100\times0.4493 = 44.93$.

Step3: Calculate the denominator

The denominator $1 + 100e^{-0.8}=1+44.93=45.93$.

Step4: Calculate the value of N

$N=\frac{10000}{45.93}\approx218$.

Answer:

218