Source:
At the end of 1993, scientists tracked 1550 nonfunctional components in orbit and projected 42 such objects are added each year. Suppose that an average of 15 of these are brought back to Earth each year.
Question.
Let t represent time in years. Write the function D that models the total number of cataloged nonfunctional components in orbit at the end of the year if 42 such objects are added each year to the initial 1550 objects in orbit.
help please?
To write the function D that models the total number of cataloged nonfunctional components in orbit at the end of the year, we need to consider two factors: the initial number of nonfunctional components and the number of objects added each year.
The initial number of nonfunctional components is given as 1550.
The number of objects added each year is given as 42.
Since the components are added each year, we can use a linear function to model the total number of components at the end of each year.
The general form of a linear function is y = mx + b, where:
- y represents the dependent variable (in this case, the total number of cataloged nonfunctional components)
- x represents the independent variable (in this case, time in years)
- m represents the slope of the line (the rate of change)
- b represents the y-intercept (the initial value)
In our case, the initial value is 1550, and the rate of change is 42 per year.
So, the function D(t) can be written as follows:
D(t) = mt + b
Substituting the given values:
D(t) = 42t + 1550
This is the function that models the total number of cataloged nonfunctional components in orbit at the end of the year.