The equation N(t) = 1900/ (1 + 200^e−0.625t) models the number of people N in a school who have heard a rumor after t days. How many people started the rumor?

Question

The equation N(t) = 1900 / (1 + 200^e−0.625t) models the number of people N in a school who have heard a rumor after t days.

How many people started the rumor?

Answer 1

N(t)= 1900 / [1 + 200e^-0.625t]

To know how many people N in the school started the rumor, we set t=0 zero days of spreading the rumor.

then; t=0        

N(0) = 1900 / [1 + 200e^-0.625(0)]

N(0) = 1900 / [1 + 200e^-0.625(0)] because e^0.625(0) = e^0 = 1

N(0) = 1900 / [1 + 200e^-0.625(0)]

N(0) = 1900 / [1 + (200 x 1)]

N(0) = 1900 / [1 + 200]

N(0) = 1900 / [201]

N(0) = 1900 / [201] =9.45

so, we get N(0) = 9.45 approx. 9.00

the number of people who started the rumor was 9 people.