Question

the amount of money in a savings account 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 account opened, x: 1, 2, 3, 4
money in account ($), f(x): 179.92, 217.63, 259.08, 312.15
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

$217.63 - 179.92 = 37.71$
$259.08 - 217.63 = 41.45$
$312.15 - 259.08 = 53.07$

Step2: Calculate exponential ratios

$\frac{217.63}{179.92} \approx 1.21$
$\frac{259.08}{217.63} \approx 1.19$
$\frac{312.15}{259.08} \approx 1.20$

Step3: Compare consistency

Linear differences vary widely; ratios are nearly constant.

Step4: Find average ratio

$\frac{1.21 + 1.19 + 1.20}{3} = 1.20$

Answer:

Exponential function would better model the data because as $x$ increases, the $y$ values change by a nearly constant multiplicative factor. The growth factor of this function is approximately 1.20.