Question

Sociologists have found that information spreads among a population at an exponential rate. Suppose that the function y=525 (1 - e^-0.038t) models the number of people in a town of 525 people who have heard news within t hours of its distribution.

Use your graphing calculator to graph the function y=525 (1 - e^-0.038t) and determine when 90% of the people will have heard about the grocery store opening.

a. 32 h
b. 61 h
c. 54 h
d. 76 h

Answer 1

b. 61h

Explanation:

Answer 2

b.

`t=61hour`

Explanation:

We are given

Sociologists have found that information spreads among a population at an exponential rate

`y=525(1-e^(-0.038t))`

Since,

initial population is 525

so, 90% of population is

`y=(90)/(100)* 525`

`y=472.5`

now, we can draw graph of both equations

and then we can find intersection point

so, we get time as

`t=61hour`