The number of unwatched shows in Sylvia's DVR is 90. The number grows by 15 unwatched shows per week. The function N(t) = 90 + 15t represents the relation between the number of unwatched shows, N, and the time, t, measured in weeks.
a. Determine the independent and dependent variable.
Independent:
Dependent:
b. Find N(3).
Sylvia will have _____ shows in her DVR after 3 weeks.
the number of shows is dependent on the number of weeks
... more weeks means more shows
a.
Independent variable: The independent variable in this scenario is time, measured in weeks. It is denoted as "t".
Dependent variable: The dependent variable is the number of unwatched shows in Sylvia's DVR. It is denoted as "N".
b.
To find N(3), we substitute t = 3 into the given function N(t) = 90 + 15t.
N(3) = 90 + 15(3)
= 90 + 45
= 135
Therefore, Sylvia will have 135 shows in her DVR after 3 weeks.
a. The independent variable is time, t (measured in weeks), as it is the variable that we have control over and is used to determine the number of unwatched shows in Sylvia's DVR. The dependent variable is the number of unwatched shows, N, since it depends on the value of the independent variable.
b. To find N(3), we substitute t = 3 into the function N(t) = 90 + 15t:
N(3) = 90 + 15(3)
N(3) = 90 + 45
N(3) = 135
Therefore, Sylvia will have 135 shows in her DVR after 3 weeks.