Question

You want to use the hot tub at the hotel you're staying at, but it's not hot enough. The hotel manager tells you they they will turn the heat up and the temperature will increase by 10% each hour.The initial temperature of the hot tub is 68°.

The hot tub heater shuts off when the water hits the standard maximum safe temperature of 104°F. For about how long did the heater run?

Answer 1

this is a geometric sequence with first term 68 and common ratio 1.1.
so the temperatures every hour are
68 , 74.8 , 82.28 ,

the next ones will be 68*1.1^3 , 68*1.1^4 etc

compute these values until you get 104 degrees.

then you can add up the number of hours that the heater ran.

Answer 2

it goes up 6.8 degrees every hour and it went up 36 degrees so how much did it go up

Answer 3

29.2

Answer 4

divide 36 by 6.8 and that is the hours it took to go up to thee max temp

Answer 5

no divide 36 by 6.8 is equal to 5.294

Answer 6

so it took the hot tub 5.3 hours to get to the max temp

Answer 7

do you understand it

Answer 8

In the last question you referred to a common ratio which would indicate its a geometric sequence so I've assumed that is this question Are you studying sequences in class at the moment . @clamin?

Answer 9

but the problem has nothing to do with a common ratio

Answer 10

it depends on how you interpret it . A similar question mentioned a common ratio.

Answer 11

you could easily just times the 68 by the 10% get the 6.8 then divide that into the 36 degree change to get the 5.3 hours

Answer 12

but why would you use a common ratio

Answer 13

because it was mentioned by clamin in the last question. She's gone now anyway.

Answer 14

the reason is that there is nothing that it can compare to to get a common ratio

Answer 15

If she is studying AS and GS sequences it might be the case. That's why i asked her.