let t represent time in years. write the function D that models the total number of nonfunctional components at the end of the year if 42 are added each year to the initialize objects .

Question

so basically this is the explaining part One particular source of space is nonfunctional spacecraft at the end of 1993 scientists tracked 1550 nonfunctional components in orbit and projected 42 such objects are added each year suppose the average of 15of these recenter the atmosphere around each year

Answer 1

Let’s look at what’s changing year on year.

42 is the number of objects projected to be non-functional by the end of each year, so 42t is the additional number projected for t years. Also, 15t is the estimated number that burn up on reentry in t years.

In 1993 1550 were tracked, so this is an initial number. The total number tracked may or may not include those that burn up. Let’s assume that 1550 doesn’t include those that burnt up. And also assume that 42 includes those that were tracked and those that burnt up. So we need to subtract 15 from 42=27 being the net number that can be detected, modelled by D(t). So D(t)=1550+27t where t is the number of years since 1993. Another way to represent this is D(t)=1550+27(t-1993) where t is the year itself.

If we assume that 1550 includes the components that burn up on re-entry, and 42 doesn’t include them, then we need to add 15 to 42=57 total components per year and D(t)=1550+57t or 1550+57(t-1993).