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)

Problem Understanding: Understand the problem. 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. 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. 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. 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 * (1.1)^6.Matching the Expression with Options: Match the expression with the given options. The correct expression we found is 550 * (1.1)^6, which matches option (B) 550(1+0.1)^(6).

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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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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) $550(1+0.1)^{6}$ .