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

b. 61h

Step-by-step explanation:

b.

Step-by-step explanation:

We are given

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

Since,

initial population is 525

so, 90% of population is

now, we can draw graph of both equations

and then we can find intersection point

so, we get time as

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).