Question

Part 2: The Zombie Assassin

Answer 1

Answer:  See below

Step-by-step explanation:

            y = a(b)ˣ

• y: final population of zombies
• a: initial population of zombies
• b: rate of decrease
• x: number of hours

Given: a = 500,000   b = 50% (0.5)    

           y = 500,000(0.5)ˣ

Since we want to know the number assassinated (A), subtract the total from the final population of zombies

A = 500,000 - y

a) Equation: 500,000 - 500,000(0.5)ˣ

b)

$\begin{array}{c|c|c||l|c}\underline{\quad a\quad}&\underline{\quad b\quad}&\underline{\quad x\quad}&\underline{\quad 500,000(0.5)^x=y \qquad}&\underline{\quad 500,000-y=A\quad}\\500,000&0.5&5&500,000(0.5)^5=15,625&\bold{484,375}\\500,000&0.5&10&500,000(0.5)^{10}=488&\bold{499,512}\\500,000&0.5&15&500,000(0.5)^{15}=15&\bold{499,985}\\500,000&0.5&20&500,000(0.5)^{20}=0&\bold{500,000}\\\end{array}$

(Graph attached)

c) The assassins will earn 100,000 + 2(499,985) = $1,099,970 after 15 hours.

The number of zombies needed to assassinate in order to earn $1,000,000:

100,000 + 2z = 1,000,000

                 2z =   900,000

                   z =   450,000

d) How long will it take to eliminate all of the zombies?

   The population of zombies is zero when x = 20 hours

   How much money did the assassinators earn?

   100,000 + 2(500,000) = $1,100,000