Solve the Problem $\$ 20,000$ Every Year Thereafter, Expenses Increase By for Year

question 248

Multiple Choice

Solve the problem.
-Expenses for a company for year 1 are $\$ 20,000$ . Every year thereafter, expenses increase by $\$ 1,500$ plus $2 \%$ of the cost of the prior year. Let $a _ { 1 }$ represent the original cost for year 1 ; that is $a _ { 1 } = 20,000$ .
Use a recursive formula to find the cost $a _ { n }$ in terms of $a _ { n - 1 }$ for each subsequent year, $\mathrm { n } \geq 2$ .

• A) \(a _ { n } = 1.02 a _ { n - 1 } + 21,500 , n \geq 2\)
• B) \(a _ { n } = 0.02 a _ { n - 1 } + 1,500 , n \geq 2\)
• C) \(a _ { n } = 1.02 a _ { n - 1 } + 1,500 , n \geq 2\)
• D) \(a _ { n } = 0.02 a _ { n - 1 } + 21,500 , n \geq 2\)

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Definitions:

Dependent Variable

A variable in an experiment or model whose value is affected by changes in other (independent) variables.

Independent Variables

Variables in a statistical or mathematical model that are manipulated or selected by the researcher to determine their effect on dependent variables.

Sample Size

The number of observations or items selected from a population to participate in a study, which can influence the study's validity and outcomes.

Correlation Coefficient

A measure indicating the degree to which two variables are linearly related, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation).