Google R & D Spending. In 2009, Google spent about $2800 million on research and development and spent $8000 million in 2013. The relationship between Google's spending and time has been linear; in the problem that follows, assume that the relationship will remain linear until 2030. a) Find a linear function that models Google's spending as a function of time. b) Use your model to predict Google's R & D spending in 2020. c) Write, including units, and interpret the slope of your model.

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**Google R & D Spending**

In 2009, Google spent about $2,800 million on research and development, and this amount increased to $8,000 million in 2013. The relationship between Google’s spending and time has been linear. Assume that this linear trend will continue until 2030. Below are the tasks that need to be addressed:

a) **Find a Linear Function**  
   Create a linear function that models Google’s R&D spending as a function of time.

b) **Prediction Using the Model**  
   Use the model to predict Google’s R&D spending in the year 2020.

c) **Slope and Interpretation**  
   Write the slope of the model, including the units, and interpret its significance.

d) **Intercepts Interpretation**  
   Write the intercepts as ordered pairs including units, and provide an interpretation of these values.

e) **Find the Inverse**  
   Determine the inverse of your linear model.

f) **Estimate Year Based on Spending**  
   Use your inverse function to estimate the year when Google’s R&D spending reached $15,800 million.

g) **Contextual Domain**  
   Establish a contextual domain for the model and justify why it is reasonable.
Transcribed Image Text:**Google R & D Spending** In 2009, Google spent about $2,800 million on research and development, and this amount increased to $8,000 million in 2013. The relationship between Google’s spending and time has been linear. Assume that this linear trend will continue until 2030. Below are the tasks that need to be addressed: a) **Find a Linear Function** Create a linear function that models Google’s R&D spending as a function of time. b) **Prediction Using the Model** Use the model to predict Google’s R&D spending in the year 2020. c) **Slope and Interpretation** Write the slope of the model, including the units, and interpret its significance. d) **Intercepts Interpretation** Write the intercepts as ordered pairs including units, and provide an interpretation of these values. e) **Find the Inverse** Determine the inverse of your linear model. f) **Estimate Year Based on Spending** Use your inverse function to estimate the year when Google’s R&D spending reached $15,800 million. g) **Contextual Domain** Establish a contextual domain for the model and justify why it is reasonable.
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