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 = 30,000 / (1 + 300e^(-0.6t)) 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? 181 (round to the nearest integer as needed.) b) how many will have heard the rumor by the end of the fifth 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 = 30,000 / (1 + 300e^(-0.6t)) 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? 181 (round to the nearest integer as needed.) b) how many will have heard the rumor by the end of the fifth day? (round to the nearest integer as needed.)

Answer

Explanation:

Step1: Substitute t = 5 into the formula

We have the formula $N=\frac{30000}{1 + 300e^{-0.6t}}$. When $t = 5$, we first calculate the exponent part: $e^{-0.6\times5}=e^{-3}$. Since $e^{-3}=\frac{1}{e^{3}}$ and $e\approx2.71828$, then $e^{-3}\approx\frac{1}{20.0855}\approx0.0498$.

Step2: Calculate the denominator

The denominator is $1+300e^{-3}$. Substitute the value of $e^{-3}$ we just found: $1 + 300\times0.0498=1+14.94 = 15.94$.

Step3: Calculate N

$N=\frac{30000}{15.94}\approx1882$.

Answer:

1882