To solve this problem, let's break down the information provided and use it to form a model of the number of lights that are on after [tex]$t$[/tex] minutes:
1. Initial Condition: When the show starts, 10 lights are on. This gives us the initial count.
2. Rate of Change: It is given that every 30 seconds, 1 more light comes on.
- First, note that 1 minute is equal to 60 seconds.
- Since every 30 seconds, 1 more light turns on, in 1 minute (which is 60 seconds), 2 more lights will turn on [tex]\( (60\, \text{seconds} \div 30\, \text{seconds/light} = 2 \, \text{lights/minute}) \)[/tex].
Given this rate:
- After 1 minute, the number of additional lights will be 2.
- After 2 minutes, the number of additional lights will be [tex]\(2 \times 2 = 4\)[/tex].
- After [tex]\(t\)[/tex] minutes, the number of additional lights will be [tex]\(2t\)[/tex].
Combining the initial count of lights and the additional lights, we get the total number of lights [tex]$L$[/tex] after [tex]$t$[/tex] minutes:
[tex]\[ L = 2t + 10 \][/tex]
Therefore, the function that models the number of lights that are on after [tex]$t$[/tex] minutes is:
[tex]\[ L = 2t + 10 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{B. \, L=2t+10} \][/tex]
