Question

the value of a certain investment 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 years since investment made, x | 1 | 2 | 3 | 4
value of investment ($), f(x) | 23,729.61 | 28,207.11 | 32,684.61 | 37,198.11

answer attempt 1 out of 2
function would better model the data because as x increases, the y values change
. the of this function is approximately

Explanation:

Step1: Calculate linear differences

$28,207.11 - 23,729.61 = 4,477.50$
$32,684.61 - 28,207.11 = 4,477.50$
$37,198.11 - 32,684.61 = 4,477.50$

Step2: Calculate exponential ratios

$\frac{28,207.11}{23,729.61} \approx 1.1887$
$\frac{32,684.61}{28,207.11} \approx 1.1587$
$\frac{37,198.11}{32,684.61} \approx 1.1381$

Step3: Compare linear vs exponential

Linear differences are constant; ratios vary.

Answer:

Linear function would better model the data because as $x$ increases, the $y$ values change by a constant amount. The common difference of this function is approximately 4477.50.