Question

a table of values is given for the number of zombies in a town ( z(t) ), ( t ) weeks, outbreak.
a. assuming that growth is linear, complete the table

( t )	0	1	2	3	4

b. write a linear model for ( z(t) ).

Explanation:

Step1: Calculate slope of linear model

Slope $m = \frac{z(2)-z(0)}{2-0} = \frac{45-5}{2} = 20$

Step2: Find z(1) using slope

$z(1) = z(0) + m = 5 + 20 = 25$

Step3: Find z(3) using slope

$z(3) = z(2) + m = 45 + 20 = 65$

Step4: Find z(4) using slope

$z(4) = z(3) + m = 65 + 20 = 85$

Step5: Write linear model (slope-intercept)

Linear form: $z(t) = mt + b$, where $b=z(0)=5$, $m=20$. So $z(t)=20t+5$

Answer:

Part a (Completed Table):

$t$	$z(t)$
1	25
2	45
3	65
4	85

Part b (Linear Model):

$z(t) = 20t + 5$