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Fidel has a rare coin worth
$550. Each decade, the coin's value increases by
10%.
Which expression gives the coin's value, 6 decades from now?
Choose 1 answer:
(A)
550*0.1^(6)
(B)
550(1+0.1)^(6)
(c)
550+(1+0.1)^(6)
(D)
550+0.1^(6)

Fidel has a rare coin worth $\$ 550$ . Each decade, the coin's value increases by $10 \%$ . $\newline$ Which expression gives the coin's value, $6$ decades from now? $\newline$ Choose $1$ answer: $\newline$ (A) $550 \cdot 0.1^{6}$ $\newline$ (B) $550(1+0.1)^{6}$ $\newline$ (C) $550+(1+0.1)^{6}$ $\newline$ (D) $550+0.1^{6}$

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Write exponential functions: word problems

Full solution

Q. Fidel has a rare coin worth

\$ 550

. Each decade, the coin's value increases by

10 \%

.

\newline

Which expression gives the coin's value,

6

decades from now?

\newline

Choose

1

answer:

\newline

(A)

550 \cdot 0.1^{6}

\newline

(B)

550(1+0.1)^{6}

\newline

(C)

550+(1+0.1)^{6}

\newline

(D)

550+0.1^{6}

Problem Understanding: Understand the problem. $\newline$ We need to find the expression that represents the value of the coin after $6$ decades, given that it increases by $10\%$ each decade. An increase of $10\%$ each decade means that the value of the coin is multiplied by $1 +$ the rate of increase $(0.1)$ each decade.
Translation of Percentage Increase: Translate the percentage increase into a growth factor. $\newline$ A $10\%$ increase can be represented as a growth factor of $1 + 0.1$ , which is $1.1$ . This means that each decade, the coin's value is multiplied by $1.1$ .
Application of Growth Factor: Apply the growth factor for $6$ decades. $\newline$ To find the value of the coin after $6$ decades, we need to multiply the initial value by the growth factor raised to the power of $6$ . This is because the coin's value is compounded each decade.
Expression with Initial Value and Growth Factor: Write the expression using the initial value and the growth factor. $\newline$ The initial value of the coin is $\$550$ , and the growth factor for each decade is $1.1$ . Therefore, the expression for the coin's value after $6$ decades is $550 \times (1.1)^6$ .
Matching the Expression with Options: Match the expression with the given options. $\newline$ The correct expression we found is $550 \times (1.1)^6$ , which matches option (B) $550(1+0.1)^{6}$ .

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\newline

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