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Javier bought a painting for
$150. Each year, the painting's value increases by a factor of 1.15 .
Which expression gives the painting's value after 7 years?
Choose 1 answer:
(A)
150+1.15*7
(B)
150*1.15^(7)
(C)
(150*1.15)^(7)
(D)
(150+1.15)*7

Javier bought a painting for $\$ 150$ . Each year, the painting's value increases by a factor of $1$ . $15$ . $\newline$ Which expression gives the painting's value after $7$ years? $\newline$ Choose $1$ answer: $\newline$ (A) $150+1.15 \cdot 7$ $\newline$ (B) $150 \cdot 1.15^{7}$ $\newline$ (C) $(150 \cdot 1.15)^{7}$ $\newline$ (D) $(150+1.15) \cdot 7$

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Write exponential functions: word problems

Full solution

Q. Javier bought a painting for

\$ 150

. Each year, the painting's value increases by a factor of

1

.

15

.

\newline

Which expression gives the painting's value after

7

years?

\newline

Choose

1

answer:

\newline

(A)

150+1.15 \cdot 7

\newline

(B)

150 \cdot 1.15^{7}

\newline

(C)

(150 \cdot 1.15)^{7}

\newline

(D)

(150+1.15) \cdot 7

Identify nature of increase: Identify the nature of the increase in the painting's value. $\newline$ The painting's value increases by a factor of $1.15$ each year, which means it is a case of exponential growth.
Determine mathematical representation: Determine the correct mathematical representation for exponential growth. $\newline$ Exponential growth is represented by the initial value $A$ multiplied by the growth factor $r$ raised to the power of the number of time periods $t$ , which can be written as $A \cdot r^{t}$ .
Match options with correct representation: Match the given options with the correct representation of exponential growth. $\newline$ Option (A) represents linear growth, which is incorrect. $\newline$ Option (B) represents the initial value multiplied by the growth factor raised to the power of $7$ , which matches the correct representation of exponential growth. $\newline$ Option (C) incorrectly raises the product of the initial value and the growth factor to the power of $7$ . $\newline$ Option (D) represents a sum multiplied by $7$ , which is also incorrect.
Choose correct option: Choose the correct option based on the analysis. $\newline$ The correct option that represents the painting's value after $7$ years is (B) $150 \times 1.15^{7}$ .

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