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?

• A. ${\left(550·0.1\right)}^6$
• B. $550{\left(1+0.1\right)}^6$
• C. $550+{\left(0.1\right)}^6$
• D. $550+{\left(1+0.1\right)}^6+{\left(1+0,1\right)}^6$

Answer 1

The correct option is B

$550{\left(1+0.1\right)}^6$

Explanation for correct option (s):

Given data:

Fidel has a rare coin worth $\$550$.

Each decade, the coin's value increases by $10\%$.

To find Which expression gives the coin's value,$6$ decades from now.

The given situation represents the exponential function as,

$y=a{\left(1+r\right)}^n$

where, $a$ is the initial value that can be expressed as $a=\$550$

$r$ is the increased rate that can be expressed as $r=10\%$

$n$ is the time that can be expressed as $n=6$

Substitute the value in the formula,

$$\begin{gathered} y=550{\left(1+10\%\right)}^6 \\ y=550{\left(1+\frac{10}{100}\right)}^6 \\ y=550{\left(1+0.1\right)}^6 \end{gathered}$$

Therefore, the correct answer is option $B$.