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Current time:0:00Total duration:3:41

Video transcript

when Quinn returned from vacation he turned the heat back on in his home he said the temperature as high as it could go q represents the temperature in Quinn's home in degrees Celsius after T minutes they said q is equal to 15 plus 0.40 what was the temperature when Quinn returned from vacation so pause this video and see if you could work this out on your own alright so they want to know the temperature and you might be a little confused say hey maybe t is for temperature no T is time in minutes temperature is Q Q represents the temperature so they really want to know is what was Q when Quinn returned from vacation well right when Quinn returned from vacation that is when t is equal to zero so this is equivalent to saying what is Q our temperature when zero minutes have elapsed well if you go back to this original equation we see that Q is equal to 15 plus 0.4 times the amount of elapsed time in minutes so that's times zero so that's just going to be 15 degrees Celsius if you're familiar with slope-intercept form you could think of it is our temperature is equal to 0.4 times the elapsed time plus 15 so T equals 0 you're left with just this term which in many cases we view as our y-intercept what is going on right when we're just getting started right when our horizontal variable is equal to 0 and our horizontal variable in this situation is elapsed time how much does the temperature increase every minute there's a couple of ways you could think about this one if you recognize this as slope-intercept form you could see that 0.4 is the slope so that says for a for every one minute change in time you're going to have an increase in temperature by 0.4 degrees Celsius so you could do it that way you could try out some values you could say all right let me see think about what Q is going to be based on T so at time T equals 0 right when you got home we already figured out that the temperature is 15 degrees Celsius at t equals 1 what happens well it's going to be 15 plus point four times one well that's just going to be fifteen point four notice when we increased our time by 1 hour temperature increased by 0.4 degrees celsius by the slope and it would happen again if we increased time by another minute if we go from 1 to 2 we would get to fifteen point eight we would increase temperature by another is zero point four how much will the temperature increase if Quinn leaves the heat on for 20 minutes pause the video and see if you can answer that all right now we have to be careful here they're not asking us what is the temperature after 20 minutes they're saying how much will the temperature increase if he leaves the heat on for 20 minutes if we just want to know what is the temperature after 20 minutes we would just say okay what is Q when T is equal to 20 so it'd be 15 plus 0.4 times 20 0.4 times 20 is 8 8 plus 15 is 23 so it's 23 degrees Celsius after 20 minutes but that's not what they're asking us there's asking how much will the temperature increase well what did we start from we started from 15 degrees Celsius and now after 20 minutes we have gone to 23 degrees Celsius so we have increased by 8 degrees Celsius or another way to think about it we have increased by this amount right over here we started at 15 and after 20 minutes we've increased by 0.4 times 20 which is 8 degrees Celsius and we're done