A large pharmaceutical company uses the function f left parenthesis x right parenthesis equals 1.457 x minus 2907 to model the amount of​ money, in billions of​ dollars, it spends each year on research and​ development, where x corresponds to the year.  Use the function to predict the amount of money it will spend in 2019.
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Part 1
The company will spend ​$

​(Round to three decimal​ places.)

To solve this problem, we'll use the given linear function $ f(x) = 1.457x - 2907 $, where $ x $ represents the year. We need to find the amount of money the company will spend in 2019.

### Step-by-Step Solution:

1. **Substitute the year into the function**:
   \[
   f(2019) = 1.457 \times 2019 - 2907
   \]

2. **Calculate the expression**:
   \[
   f(2019) = 1.457 \times 2019 - 2907
   \]
   \[
   f(2019) = 2943.183 - 2907
   \]
   \[
   f(2019) = 36.183
   \]

3. **Round to three decimal places**:
   \[
   \text{The company will spend } \textbf{\$36.183 \text{ billion}} \text{ in 2019.}
   \]

So, the company will spend approximately **\$36.183 billion** on research and development in 2019.

Would you like any further details or have any additional questions? 

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Here are some related questions to expand your understanding:

1. How would the amount spent change if the coefficient 1.457 increased to 2?
2. What does the value -2907 represent in this context?
3. How would you calculate the amount spent in a different year, say 2025?
4. What year would result in the company spending \$50 billion?
5. How much would the company spend in the year 2000?
6. What would be the interpretation if the function was $ f(x) = 1.457x + 2907 $ instead?
7. What does the slope of the function tell us about the company's spending trends?
8. If the company aims to spend \$100 billion, in what year will that happen?

**Tip**: When solving problems involving linear functions, always interpret the slope and y-intercept in the context of the problem to understand the model's behavior.

Learn how to predict future spending on research and development using linear functions. Solve the problem of predicting the amount of money a pharmaceutical company will spend in 2019 based on its historical spending pattern. Understand the application of linear functions in modeling financial data. Suitable for high school students studying algebra and linear functions.

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