Exercise 18 Page 592

a From the exercise we know that the fraction of students who has heard the rumor triples every hour. This must mean that the multiplier is

3 .

b Since the fraction of students that has heard the rumor triples every hour, we can find the fraction of students that knows the rumor at

2

p.m. by dividing

100 %

3 .

\frac{1 0 0 %}{3} \approx 33 %

The fraction of students who had heard the rumor by

2

p.m. was about

33 % .

c The number of people that has heard the rumor can be described with an exponential function.

y = a b^{n}

In this function,

a

is the initial value and

b

is the multiplier. From Part A, we know that the multiplier is

3 .

With this information, we can write the equation.

y = a (3)^{n}

d From the exercise we know that it took

7

hours for the rumor to spread to the whole school. This can be interpreted as the data point

(7, 1) .

If we substitute this point into the function from Part C, we can find the initial value,

a .

y = a (3)^{n}

$n = 7$ , $y = 1$

1 = a (3)^{7}

Calculate power

1 = a (2187)

$LHS / 2187 = RHS / 2187$

\frac{1}{2 1 8 7} = a

Rearrange equation

a = \frac{1}{2 1 8 7}

e From Part D we know that the fraction of students who started the rumor was

\frac{1}{2 1 8 7} .

If this fraction equals

3

students, we can write the following proportion where

x

is the total number of students at the school.

\frac{3}{x} = \frac{1}{2 1 8 7}

Let's solve this proportion for

x .

\frac{3}{x} = \frac{1}{2 1 8 7}

$LHS \cdot x = RHS \cdot x$

3 = \frac{1}{2 1 8 7} \cdot x

$LHS \cdot 2187 = RHS \cdot 2187$

6561 = 1 \cdot x

$1 \cdot a = a$

6561 = x

Rearrange equation

x = 6561

11.1.1 Introduction to Constructions p.587-589

11.1.2 Constructing Bisectors p.592-593

11.1.3 More Explorations with Constructions p.597-599