Question

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:
Choose 1 answer:
(Choice A)
\[550\cdot 0.1^6\]
A
\[550\cdot 0.1^6\]
(Choice B)
\[550(1+0.1)^6\]
B
\[550(1+0.1)^6\]
(Choice C)
\[550+0.1^6\]
C
\[550+0.1^6\]
(Choice D)
\[550+(1+0.1)^6\]
D
\[550+(1+0.1)^6\]

Answer 1

To find the value of the coin 6 decades from now, we start with its current value of \$550. Since the coin's value increases by 10% each decade, we can express the value after 6 decades using the formula for exponential growth:

\[
\text{Future Value} = \text{Present Value} \times (1 + \text{rate})^{\text{number of periods}}
\]

In this case, the present value is \$550, the rate is 10% (or 0.1), and the number of periods is 6 decades. Therefore, we have:

\[
\text{Future Value} = 550 \times (1 + 0.1)^6
\]

This simplifies to:

\[
\text{Future Value} = 550(1.1)^6
\]

The correct choice that represents the value of the coin after 6 decades is:

**(Choice B)** \( 550(1 + 0.1)^6 \)