Problema Solution
One source of space debris is nonfunctional spacecraft. At the end of 1993, scientists tracked 1550 nonfunctional components in orbit at the end of the year if 50 such objects are added each year. Suppose that on average 1 of these are brought back to the earth each year.
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 50 such objects are added each year to the initial 1550 objects in orbit.
Answer provided by our tutors
in the year of 1993 we have:
t = 1993
D(1993) = 1550
in the year of 1994 we have:
t = 1994
D(1994) = 1550 + 50 = 1550 + (1994 - 1993)*50
in the year of 1995 we have:
t = 1995
D(1995) = 1550 + (1994 - 1993)*50 + 50 = 1550 + (1995 - 1993)*50
lets generalize:
D(t) = 1550 + (t - 1993)50
D(t) = 50t - 98,100
the can be proven using the method of Mathematical Induction.