The expression 11(1.022)^(t) models the per capita gross domestic product (GDP) of the US, in thousands of dollars, as a function of the number of years since 1950 . What does 1.022 represent in this expression? Choose 1 answer: (A) The per capita GDP in the US was $1022 in 1950. (B) The maximum per capita GDP occurred 1.022 years after 1950 . (C) The per capita GDP in the US is multiplied by approximately 1.022 each year.

Nature of Expression: The expression given is 11(1.022)^(t), where t represents the number of years since 1950. To understand what 1.022 represents, we need to consider the nature of the expression. This is an exponential function, where the base of the exponent (1.022) indicates the rate of change per year.Analysis of Options: If we look at the options provided, we can analyze each one: (A) Suggests that the per capita GDP was $1022 in 1950. However, the number 11 in the expression is the coefficient that would represent the initial value in 1950, not 1.022. (B) Suggests that the maximum per capita GDP occurred 1.022 years after 1950. This does not make sense in the context of the expression, as 1.022 is not a measure of time but a growth factor. (C) Suggests that the per capita GDP in the US is multiplied by approximately 1.022 each year. This aligns with the nature of an exponential growth model, where the base of the exponent represents the growth rate.Conclusion: Based on the analysis, we can conclude that 1.022 represents the annual growth factor of the per capita GDP. This means that each year, the per capita GDP is multiplied by 1.022, indicating an approximate 2.2% increase per year (since 1.022 is approximately 1 + 0.022, and 0.022 is 2.2%).

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The expression $11(1.022)^{t}$ models the per capita gross domestic product (GDP) of the US, in thousands of dollars, as a function of the number of years since $1950$ . $\newline$ What does $1$ . $022$ represent in this expression? $\newline$ Choose $1$ answer: $\newline$ (A) The per capita GDP in the US was $\$ 1022$ in $1950$ . $\newline$ (B) The maximum per capita GDP occurred $1$ . $022$ years after $1950$ . $\newline$ (C) The per capita GDP in the US is multiplied by approximately $1$ . $022$ each year.

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Grade 7

Evaluate two-variable equations: word problems

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Q. The expression

11(1.022)^{t}

models the per capita gross domestic product (GDP) of the US, in thousands of dollars, as a function of the number of years since

1950

\newline

What does

1

022

represent in this expression?

\newline

Choose

1

answer:

\newline

(A) The per capita GDP in the US was

\$ 1022

1950

\newline

(B) The maximum per capita GDP occurred

1

022

years after

1950

\newline

1

022

each year.

Nature of Expression: The expression given is $11(1.022)^{t}$ , where $t$ represents the number of years since $1950$ . To understand what $1.022$ represents, we need to consider the nature of the expression. This is an exponential function, where the base of the exponent $(1.022)$ indicates the rate of change per year.
Analysis of Options: If we look at the options provided, we can analyze each one: $\newline$ (A) Suggests that the per capita GDP was $\$1022$ in $1950$ . However, the number $11$ in the expression is the coefficient that would represent the initial value in $1950$ , not $1.022$ . $\newline$ (B) Suggests that the maximum per capita GDP occurred $1.022$ years after $1950$ . This does not make sense in the context of the expression, as $1.022$ is not a measure of time but a growth factor. $\newline$ (C) Suggests that the per capita GDP in the US is multiplied by approximately $1.022$ each year. This aligns with the nature of an exponential growth model, where the base of the exponent represents the growth rate.
Conclusion: Based on the analysis, we can conclude that $1.022$ represents the annual growth factor of the per capita GDP. This means that each year, the per capita GDP is multiplied by $1.022$ , indicating an approximate $2.2\%$ increase per year (since $1.022$ is approximately $1 + 0.022$ , and $0.022$ is $2.2\%$ ).