A small town has 2000 inhabitants. At 8 AM, 160 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor? (Do not round k in your calculation. Round your final answer to one decimal place.)

3:36 PM

Step-by-step explanation:

Let fraction (y) of the people that heard the rumor , the differential equation that is satisfied by the by y is,

Solving the differential equation,

The total number of inhabitants of the town = 2000

The number of people that  heard the rumor = 160

At 8 AM, let t = 0,

                       = 0.08

By noon, half of the town as heard the rumor.

Then,    

Therefore,

              k ≈ 0.06106

Calculating time, t when y(t) = 90%

        ⇒ y(t) = 0.9

              t = 7.59 hours

              ⇒ 7 hours 36 minutes

From 8 A.M. plus 7 hours 36 minutes = 3:36 PM

At 3:36 PM will 90% of the population have heard the rumor

step-by-step explanation:

i found the koficent of the linear function and i foun c acordind to the strict formula y=kx+c and then i took 2 as an x and replacet it on the formula i found and then foun the y