What we know: 12 hour period from 8pm to 8am temperature dropped from 8°F to 16°F from 8pm to 8am
We need to find temperature at 4 am.
We can start by setting up points: 8pm is are starting point with 8°F, we can express it as (0,8), 0 represents initial time from 0 to 12 hour span. 8am is the ending point with 16°F, we can express it as (12,16), 12 represents the end time of 0 to 12 hours span. We will use these points to find slope. slope=m=(16-8)/(12-0)=8/12=2/3
Now, we can set up an expression to find any temperature at a specific time. Aslo, x represents the hours not the the specific time of 4am. We will use 8 since 4am is the 8th hour of the 12 hour span. Using slope of 2/3 and the y intercept of (0,8) since we were already at 8°F at the initial time of 0 we have the function:
