Question

The number, N, of people who have heard a rumor spread by mass media by time tt is modeled by

N(t)=a(1 - e⁻ᵏᵗ).

There are 100,000 people in the population who hear the rumor eventually. If 15% of them heard it the first day, find a and k, assuming t is measured in days.

Answer 1

To find the values of a and k in the equation N(t) = a(1 - e^-kt), we can use the given information about the number of people who have heard the rumor by time t and the percentage of people who heard it on the first day.

Step-by-step explanation:

To find the values of a and k, we can plug in the given information into the equation N(t) = a(1 - e^-kt).

We know that N(t) represents the number of people who have heard the rumor by time t, and we are told that eventually 100,000 people hear the rumor. So we can plug in N(t) = 100,000.

We also know that 15% of the total population heard the rumor on the first day, so when t = 1, N(t) should be equal to 15% of the total population. Plugging in N(t) = 0.15 * 100,000 = 15,000 when t = 1, we can solve for a.

Finally, we can find k by plugging in the values of a and N(t) into the equation and solving for k using logarithms.