Question

Alesia inherited a savings account that was started by her grandmother 30 years ago. This scenario is modeled by the function A(m) = 4700(1.22)^(m+30), where A(m) represents the value of the account, in dollars, m years after the inheritance. Which function below is equivalent to A(m)?

Answer 1

Option 3

Step-by-step explanation

We have that the function that represents the value of the inheritance is:

`A(m)=4700(1.22)^{(m\text{ + 30)}}`

To find an equivalent ratio, we have to understand the law of indices that states that:

`x^{\text{a + b}}=x^{a^{}}\cdot x^b`

So, we can split the function as:

`\begin{gathered} A(m)\text{ = 4700 }\cdot(1.22)^{m\text{ + 30}} \\ \Rightarrow\text{ A(m) = 4700 }\cdot(1.22)^m\cdot(1.22)^(30) \\ \Rightarrow A(m)=4700(1.22)^m(1.22)^(30) \end{gathered}`

The answer is Option 3.