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The expression
1.5*1.09^(t) models the housing costs, in thousands of dollars, for summer term
t years since Chinedu applied to his college.
What does 1.09 represent in this expression?
Choose 1 answer:
(A) The summer housing costs were
$1,090 the year that Chinedu applied to his college.
(B) Chinedu applied to his school 9 years ago.
(C) The summer housing costs increase by
9% each year.

The expression $1.5 \cdot 1.09^{t}$ models the housing costs, in thousands of dollars, for summer term $t$ years since Chinedu applied to his college. $\newline$ What does $1$ . $09$ represent in this expression? $\newline$ Choose $1$ answer: $\newline$ (A) The summer housing costs were $\$ 1,090$ the year that Chinedu applied to his college. $\newline$ (B) Chinedu applied to his school $9$ years ago. $\newline$ (C) The summer housing costs increase by $9 \%$ each year.

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Write exponential functions: word problems

Full solution

Q. The expression

1.5 \cdot 1.09^{t}

models the housing costs, in thousands of dollars, for summer term

t

years since Chinedu applied to his college.

\newline

What does

1

.

09

represent in this expression?

\newline

Choose

1

answer:

\newline

(A) The summer housing costs were

\$ 1,090

the year that Chinedu applied to his college.

\newline

(B) Chinedu applied to his school

9

years ago.

\newline

(C) The summer housing costs increase by

9 \%

each year.

Identify components of expression: Identify the components of the expression. $\newline$ The expression given is $1.5 \times 1.09^{t}$ . This is a typical exponential growth model where $1.5$ represents the initial value and $1.09^{t}$ represents the growth factor over time $t$ .
Understand growth factor: Understand the growth factor. $\newline$ The base of the exponent, $1.09$ , represents the annual growth rate of the housing costs. Since the base is greater than $1$ , it indicates a percentage increase each year.
Convert growth factor to percentage: Convert the growth factor to a percentage. $\newline$ To interpret the growth factor, subtract $1$ from the base of the exponent and then multiply by $100$ to convert it to a percentage. $(1.09 - 1) \times 100\% = 0.09 \times 100\% = 9\%$ .
Match growth factor to answer choices: Match the growth $\%$ to the answer choices. $\newline$ The growth percent of $9\%$ matches with the statement that the summer housing costs increase by $9\%$ each year.

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