Because of the use of lithium batteries in all forms of​ applications, the demand for lithium is projected to steadily increase. Using data from 2017 and projected to​ 2025, the function Upper D equals 23.5 t plus 171.3 can be used to model the demand for lithium in metric​ tons, where t is the number of years after 2015. Complete parts ​(a) through ​(c).

Question

What is the slope of the graph of this​ function?
The slope is
  
enter your response here. ​(Type an integer or a​ decimal.)
Part 3
​(c) What is the​ D-intercept of the graph of this​ function?
The​ D-intercept is
  
enter your response here. ​(Type an integer or a​ decimal.)

Answer 1

Let's analyze the given linear demand function:

\[ D = 23.5t + 171.3 \]

where \( D \) is the demand in metric tons, and \( t \) is the number of years after 2015.

Part (a): Finding the slope of the graph

The slope of a linear function in the form \( y = mx + b \) is represented by \( m \). In this case, the coefficient of \( t \) (which represents the number of years after 2015) is:

\[ \text{slope} = 23.5 \]

Part (b): Finding the D-intercept

The D-intercept occurs when \( t = 0 \) (which corresponds to the year 2015). We can find the D-intercept by substituting \( t = 0 \) into the demand function:

\[ D = 23.5(0) + 171.3 \] \[ D = 171.3 \]

Summary of Answers

• Slope: 23.5
• D-intercept: 171.3

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