Answer :
For both problems, there's one variable that that depends on another one,
and you have to write the equation that shows how they're connected.
For #21:
Step #1:
Fold your hands in your lap, and stare at the numbers in the table for a while.
-- In the first 3 hours, the temperature rises 6 degrees.
-- In the first 5 hours, the temperature rises 10 degrees.
-- In the first 9 hours, the temperature rises 18 degrees.
Do you notice that the temperature is rising 2 degrees every hour ?
So maybe the equation is: Temperature = 2 x time.
If that's correct, then it'll work on any line in the table.
Try it out on the first line, where the time is zero and the temperature is 56.
Temperature = 2 x time
56 = 2 x 0 Is this true ? I don't think so.
The equation is not that simple, because the temperature didn't start out
at zero when the time was zero. The temperature had a head start. It was
56 when the time was zero.
The correct equation is: Temperature = (2 x time) + 56
That way, when time = zero, temperature = 56.
Check it out on another line in the table. Try the line where time is 5 hours.
Temperature = (2 x time) + 56
66 = (2 x 5) + 56
66 = 10 + 56
66 = 66 YAY ! The equation works !
Temperature = (2 x time) + 56 is the equation for part (a).
(b). What's the temperature after 12 hours ? Use your equation:
Temperature = (2 x time) + 56
Temperature = (2 x 12) + 56
Temperature = 24 + 56
Temperature = 80 degrees F.
=====================================
For #22:
The table from #21 is NOT used in #22.
#22 stands all alone.
It says that the the surface of the lake starts out at 648 feet, and
it drops 3 inches per day. Again, you have to make up the equation
that shows how the surface level is related to the number of days.
Before we go any farther, everything in the equation has to be in the
same units, otherwise we'll get all tangled up and we'll be in trouble.
So right now, let's just notice that 3 inches is the same as 1/4 foot.
Now the daily drop is in the same units as the surface level of the lake.
-- The level drops 1/2 foot every day. So you might think that maybe the
equation should be: Surface level = ( -1/4) times (days).
If that's the correct equation, then on day-zero, the level is (-1/4) x (0) = 0
That's not true, because the level is 648 feet on day-zero. So the correct
equation is
Surface level = ( -1/4) x (days) + 648 (a).
(b). What is the level after 21 days ? Use your equation.
Surface level = ( -1/4) x (days) + 648
Surface level = ( -1/4) x (21) + 648
Surface level = - 21/4 + 648
21/4 = 5.25
Surface level = -5.25 + 648
Surface level = 642.75 feet
and you have to write the equation that shows how they're connected.
For #21:
Step #1:
Fold your hands in your lap, and stare at the numbers in the table for a while.
-- In the first 3 hours, the temperature rises 6 degrees.
-- In the first 5 hours, the temperature rises 10 degrees.
-- In the first 9 hours, the temperature rises 18 degrees.
Do you notice that the temperature is rising 2 degrees every hour ?
So maybe the equation is: Temperature = 2 x time.
If that's correct, then it'll work on any line in the table.
Try it out on the first line, where the time is zero and the temperature is 56.
Temperature = 2 x time
56 = 2 x 0 Is this true ? I don't think so.
The equation is not that simple, because the temperature didn't start out
at zero when the time was zero. The temperature had a head start. It was
56 when the time was zero.
The correct equation is: Temperature = (2 x time) + 56
That way, when time = zero, temperature = 56.
Check it out on another line in the table. Try the line where time is 5 hours.
Temperature = (2 x time) + 56
66 = (2 x 5) + 56
66 = 10 + 56
66 = 66 YAY ! The equation works !
Temperature = (2 x time) + 56 is the equation for part (a).
(b). What's the temperature after 12 hours ? Use your equation:
Temperature = (2 x time) + 56
Temperature = (2 x 12) + 56
Temperature = 24 + 56
Temperature = 80 degrees F.
=====================================
For #22:
The table from #21 is NOT used in #22.
#22 stands all alone.
It says that the the surface of the lake starts out at 648 feet, and
it drops 3 inches per day. Again, you have to make up the equation
that shows how the surface level is related to the number of days.
Before we go any farther, everything in the equation has to be in the
same units, otherwise we'll get all tangled up and we'll be in trouble.
So right now, let's just notice that 3 inches is the same as 1/4 foot.
Now the daily drop is in the same units as the surface level of the lake.
-- The level drops 1/2 foot every day. So you might think that maybe the
equation should be: Surface level = ( -1/4) times (days).
If that's the correct equation, then on day-zero, the level is (-1/4) x (0) = 0
That's not true, because the level is 648 feet on day-zero. So the correct
equation is
Surface level = ( -1/4) x (days) + 648 (a).
(b). What is the level after 21 days ? Use your equation.
Surface level = ( -1/4) x (days) + 648
Surface level = ( -1/4) x (21) + 648
Surface level = - 21/4 + 648
21/4 = 5.25
Surface level = -5.25 + 648
Surface level = 642.75 feet
