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

Answer:

b.

$t=61hour$

Step-by-step 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

$y=\frac{90}{100}\times 525$

$y=472.5$

now, we can draw graph of both equations

and then we can find intersection point

so, we get time as

$t=61hour$