Questions: The amount of money in Candace's savings account (in dollars) can be modeled by the following function: A(x)=1600(1.0021)^x where x is the number of months since Candace opened this account. Write the domain and range of the function, given the real-world context, using inequality symbols. Domain: x ? 0 Range: A(x) ? 0

The amount of money in Candace's savings account (in dollars) can be modeled by the following function:
A(x)=1600(1.0021)^x
where x is the number of months since Candace opened this account. Write the domain and range of the function, given the real-world context, using inequality symbols.

Domain: x ? 0 Range: A(x) ? 0

Transcript text: The amount of money in Candace's savings account (in dollars) can be modeled by the following function: \[ A(x)=1600(1.0021)^{x} \] where $x$ is the number of months since Candace opened this account. Write the domain and range of the function, given the real-world context, using inequality symbols. Domain: $\boldsymbol{x}$ $\square$ $? 0$ $\square$ Range: $A(x)$ \[ ? 0 \] $\square$ Submit Question

Solution

Solution Steps

Step 1: Understand the function and its context

The function $ A(x) = 1600(1.0021)^x $ models the amount of money in Candace's savings account, where $ x $ represents the number of months since the account was opened. The base amount is $ 1600 $ dollars, and the account grows at a rate of $ 1.0021 $ per month.

Step 2: Determine the domain

The domain of the function represents the possible values of $ x $. Since $ x $ is the number of months since the account was opened, it must be a non-negative real number. Therefore: \[ x \geq 0 \]

Step 3: Determine the range

The range of the function represents the possible values of $ A(x) $. Since the account starts with $ 1600 $ dollars and grows exponentially, the minimum value of $ A(x) $ is $ 1600 $ dollars. As $ x $ increases, $ A(x) $ increases without bound. Therefore: \[ A(x) \geq 1600 \]