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the amount of money in a savings account over time is given in the tabl…

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 …

Kategorie: statistics Aktualisiert: 2026-02-08

Aufgabe

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 |.

Lösungsschritte

  1. Understand the 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 |.

  2. 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.

  3. Final 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.

Antwort

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.

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.

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Question Analysis

Subject mathematics
Sub Subject statistics
Education Level high school
Difficulty unspecified
Question Type with chart, calculation
Multi Question No
Question Count 1
Analysis Status completed
Analyzed At 2026-02-08T14:50:16

OCR Text

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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 |.

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