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The expression
1350(1.05)^(t) models the average wages, in dollars, in the US as a function of the number of years since 1930 .
What does 1.05 represent in this expression?
Choose 1 answer:
(A) The average wages double every 1.05 years.
B) The average wages in the US were about
$1.05 in 1930.
(c) The average wages in the US increase by about
5% each year.

The expression $1350(1.05)^{t}$ models the average wages, in dollars, in the US as a function of the number of years since $1930$ . $\newline$ What does $1$ . $05$ represent in this expression? $\newline$ Choose $1$ answer: $\newline$ (A) The average wages double every $1$ . $05$ years. $\newline$ (B) The average wages in the US were about $\$ 1.05$ in $1930$ . $\newline$ (C) The average wages in the US increase by about $5 \%$ each year.

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Write exponential functions: word problems

Full solution

Q. The expression

1350(1.05)^{t}

models the average wages, in dollars, in the US as a function of the number of years since

1930

.

\newline

What does

1

.

05

represent in this expression?

\newline

Choose

1

answer:

\newline

(A) The average wages double every

1

.

05

years.

\newline

(B) The average wages in the US were about

\$ 1.05

in

1930

.

\newline

(C) The average wages in the US increase by about

5 \%

each year.

Expression Structure: The expression given is $1350(1.05)^{t}$ , where $t$ represents the number of years since $1930$ . To understand what $1.05$ represents, we need to look at the structure of the expression. It is an exponential function, where the base of the exponent $(1.05)$ indicates the rate of change per year.
Rate of Change: In the context of the problem, since the base of the exponent is greater than $1$ , it suggests that the quantity is increasing over time. Specifically, a base of $1.05$ indicates a $5\%$ increase each year because $1.05$ can be thought of as $100\%$ (the original amount) plus $5\%$ (the increase).
Evaluation of Options: Now, let's evaluate the options given: $\newline$ (A) The average wages double every $1.05$ years. - This is incorrect because the expression does not imply doubling; it implies a steady growth rate. $\newline$ (B) The average wages in the US were about $\$1.05$ in $1930$ . - This is incorrect because the $1.05$ is not a dollar amount; it's a multiplier for the growth rate. $\newline$ (C) The average wages in the US increase by about $5\%$ each year. - This is correct because the base of the exponent $(1.05)$ represents a $5\%$ increase.

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