Select The Correct Answer From Each Drop-down Menu.Let F ( T F(t F ( T ] Be The Sales Of A Gaming Product, In Thousands Of Units, After T T T Months. F ( T ) = 5 T + 11 F(t) = 5t + 11 F ( T ) = 5 T + 11 So, F ( 3 ) = □ F(3) = \square F ( 3 ) = □ . This Means That □ \square □ , The

Select the Correct Answer from Each Drop-Down Menu: A Mathematics Problem

Understanding the Problem

In this problem, we are given a function $f(t)$ that represents the sales of a gaming product in thousands of units after $t$ months. The function is defined as $f(t) = 5t + 11$. We are asked to find the value of $f(3)$, which means we need to substitute $t = 3$ into the function and evaluate the result.

The Function and Its Application

The function $f(t) = 5t + 11$ is a linear function, which means it has a constant rate of change. In this case, the rate of change is $5$, which represents the increase in sales for every additional month. The constant term $11$ represents the initial sales, which is the sales at $t = 0$.

To find the value of $f(3)$, we need to substitute $t = 3$ into the function. This means we need to replace $t$ with $3$ in the equation $f(t) = 5t + 11$. The result will be $f(3) = 5(3) + 11$.

Evaluating the Function

Now, let's evaluate the function $f(3) = 5(3) + 11$. To do this, we need to follow the order of operations (PEMDAS):

1. Multiply $5$ and $3$: $5(3) = 15$
2. Add $11$ to the result: $15 + 11 = 26$

Therefore, the value of $f(3)$ is $26$.

Conclusion

In this problem, we were given a function $f(t) = 5t + 11$ that represents the sales of a gaming product in thousands of units after $t$ months. We were asked to find the value of $f(3)$, which means we need to substitute $t = 3$ into the function and evaluate the result. By following the order of operations, we found that the value of $f(3)$ is $26$.

Key Takeaways

• The function $f(t) = 5t + 11$ is a linear function that represents the sales of a gaming product in thousands of units after $t$ months.
• The rate of change of the function is $5$, which represents the increase in sales for every additional month.
• The constant term $11$ represents the initial sales, which is the sales at $t = 0$.
• To find the value of $f(3)$, we need to substitute $t = 3$ into the function and evaluate the result.

Solving Similar Problems

If you are given a function in the form $f(t) = at + b$, where $a$ and $b$ are constants, you can use the same steps to find the value of the function at a specific value of $t$. Simply substitute the value of $t$ into the function and evaluate the result.

Example

Suppose we are given the function $f(t) = 2t + 4$ and we need to find the value of $f(5)$. To do this, we need to substitute $t = 5$ into the function and evaluate the result:

$f(5) = 2(5) + 4$ $f(5) = 10 + 4$ $f(5) = 14$

Therefore, the value of $f(5)$ is $14$.

Conclusion

In this article, we discussed how to select the correct answer from each drop-down menu by evaluating a function at a specific value of $t$. We used the function $f(t) = 5t + 11$ to find the value of $f(3)$, and we followed the order of operations to evaluate the result. We also discussed how to solve similar problems by substituting the value of $t$ into the function and evaluating the result.
Q&A: Evaluating Functions and Selecting the Correct Answer

Understanding Functions

A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). In the context of this problem, the function $f(t) = 5t + 11$ represents the sales of a gaming product in thousands of units after $t$ months.

Q: What is the rate of change of the function?

A: The rate of change of the function is $5$, which represents the increase in sales for every additional month.

Q: What is the initial sales represented by the function?

A: The initial sales represented by the function is $11$, which is the sales at $t = 0$.

Q: How do I evaluate the function at a specific value of $t$?

A: To evaluate the function at a specific value of $t$, you need to substitute the value of $t$ into the function and follow the order of operations (PEMDAS).

Q: What is the value of $f(3)$?

A: The value of $f(3)$ is $26$, which is found by substituting $t = 3$ into the function and evaluating the result.

Q: How do I find the value of $f(5)$?

A: To find the value of $f(5)$, you need to substitute $t = 5$ into the function and evaluate the result:

$f(5) = 2(5) + 4$ $f(5) = 10 + 4$ $f(5) = 14$

Therefore, the value of $f(5)$ is $14$.

Q: What if I have a function in the form $f(t) = at + b$? How do I evaluate it at a specific value of $t$?

A: To evaluate a function in the form $f(t) = at + b$ at a specific value of $t$, you need to substitute the value of $t$ into the function and follow the order of operations (PEMDAS).

Q: Can I use the same steps to evaluate a function with a different rate of change?

A: Yes, you can use the same steps to evaluate a function with a different rate of change. The only difference is that you will need to substitute the new rate of change into the function.

Q: What if I have a function with a negative rate of change? How do I evaluate it at a specific value of $t$?

A: To evaluate a function with a negative rate of change at a specific value of $t$, you need to substitute the value of $t$ into the function and follow the order of operations (PEMDAS). The negative rate of change will affect the direction of the function, but the steps for evaluating it remain the same.

Conclusion

In this Q&A article, we discussed how to evaluate functions and select the correct answer from each drop-down menu. We used the function $f(t) = 5t + 11$ to find the value of $f(3)$ and $f(5)$, and we followed the order of operations to evaluate the results. We also discussed how to solve similar problems by substituting the value of $t$ into the function and evaluating the result.

Key Takeaways

• A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range).
• The rate of change of a function represents the increase in output for every additional input.
• To evaluate a function at a specific value of $t$, you need to substitute the value of $t$ into the function and follow the order of operations (PEMDAS).
• You can use the same steps to evaluate a function with a different rate of change or a negative rate of change.

Solving Similar Problems

If you are given a function in the form $f(t) = at + b$, where $a$ and $b$ are constants, you can use the same steps to find the value of the function at a specific value of $t$. Simply substitute the value of $t$ into the function and evaluate the result.

Example

Suppose we are given the function $f(t) = 3t - 2$ and we need to find the value of $f(4)$. To do this, we need to substitute $t = 4$ into the function and evaluate the result:

$f(4) = 3(4) - 2$ $f(4) = 12 - 2$ $f(4) = 10$

Therefore, the value of $f(4)$ is $10$.