Given:
number lights on when the show starts = 10
the rate at which the light comes on = 30 seconds per light
t = time in minutes
L = number of lights on
To find:
the function that bests models the number of lights after t minutes
To determine the function, we will apply linear function formula:
[tex]\begin{gathered} y\text{ = mx + b} \\ b\text{ = initial amount} \\ m\text{ = rate } \\ x\text{ = t } \\ y\text{ = L} \end{gathered}[/tex]The initial number of lights = 10
b = 10
since t is in minutes, we need to convert the rate from seconds to minutes
30 seconds = 1 light
60 seconds = 2(30 seconds)
60 seconds = 2(1) = 2 lights
rate = m = 2 lights/min
substitute the values:
[tex]L\text{ =2}t\text{ + 10 \lparen option B\rparen}[/tex]