# Sociologists have found that information spreads among a population at an exponential rate. Graph the function on a graphing calculator.

Sociologists have found that information spreads among a population at an exponential rate. Suppose that the function $y=525\left(1-{e}^{-0.038t}\right)$ models the number of people in a town of 525 people who have heard news within t hours of its distribution. Graph the function on a graphing calculator. When will 90% of the people have heart about the grocery store opening?

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Step 1
Determine the $90\mathrm{%}$ of the people on the town:
$=0.9×525=472.5$
then graph $y=472.5$
the x coordinate of intersection point represent the time required for the $90\mathrm{%}$ to hear the opening
conclude that $t\approx 61$ hour
Step 2