Question

the approximate number of zombies in a certain city over time is given in the table below. answer the questions below to explain what kind of function would better model the data, linear or exponential.

number of hours since zombies first spotted, x	1	2	3	4

answer attempt 1 out of 2

function would better model the data because as x increases, the y values change
. rounded to the nearest.5, the of this

Explanation:

Step1: Check linear differences

Calculate differences between consecutive $f(x)$ values:
$143 - 34 = 109$
$554 - 143 = 411$
$2285 - 554 = 1731$

Step2: Check exponential ratios

Calculate ratios of consecutive $f(x)$ values:
$\frac{143}{34} \approx 4.21$
$\frac{554}{143} \approx 3.87$
$\frac{2285}{554} \approx 4.12$

Step3: Compare patterns

Linear models have constant differences; here differences grow rapidly. Exponential models have constant (approximate) ratios; here ratios are close to 4.0.

Answer:

Exponential function would better model the data because as $x$ increases, the $y$ values change by an approximately constant multiplicative factor. Rounded to the nearest .5, the common ratio of this function is 4.0.