Find the Maclaurin Series for the Given Function $e ^ { 4 x }$

question 17

Multiple Choice

Find the Maclaurin series for the given function.
- $e ^ { 4 x }$

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { 4 ^ { n } x ^ { n } } { n ! }\)
• B) \(\sum _ { \mathrm { n } = 0 } ^ { \infty } \frac { ( - 1 ) ^ { \mathrm { n } } 4 ^ { \mathrm { n } } \mathrm { x } ^ { \mathrm { n } } } { \mathrm { n } ! }\)
• C) \(\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } 4 ^ { n } x ^ { n } } { n ! }\)
• D) \(\sum _ { n = 1 } ^ { \infty } \frac { 4 ^ { n } x ^ { n } } { n ! }\)

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Definitions:

Saving

The portion of income that is not spent on consumption but instead is set aside for future use or investment.

Disposable Income

Income left for households to direct into savings and spending after deductions of income taxes.

APC

APC, or Average Propensity to Consume, is the ratio of total consumption to total disposable income, indicating how much income is spent.

Induced Consumption

The portion of consumer spending that changes in response to changes in disposable income.