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- WE WANT TO WRITE A LINEAR MODEL FOR THE GIVEN SITUATION.
AFTER VISITING THE SUNKEN TREASURE,
CAPTAIN HOOK TAKES THE M4 SUBMARINE BACK TO THE SURFACE.
IT STARTS 1,500 METERS BELOW THE SURFACE OF THE WATER,
AND ASCENDS AT 40 METERS PER MINUTE.
WE WANT TO WRITE AN EQUATION
TO MODEL THE DEPTH OF THE SUBMARINE.
WE WANT TO USE M FOR THE METERS BELOW THE SURFACE,
AND T FOR TIME IN MINUTES.
SO SOME OF THE KEY INFORMATION HERE
IS THAT SUBMARINE STARTS 1,500 METERS BELOW THE SURFACE,
AND THE SUBMARINE DESCENDS AT 40 METERS PER MINUTE.
AND SINCE THE STARTING POSITION
IS BELOW THE SURFACE OF THE WATER,
GOING TO REPRESENT THE STARTING POSITION
AS -1,500 METERS,
AND THEN THE RATE OF CHANGE OF THE POSITION
IS GOING TO BE +40 METERS PER SECOND,
BECAUSE THE SUBMARINE ASCENDING
OR APPROACHING THE SURFACE.
SO IF WE WANT TO HAVE AN EQUATION AND MODEL THE DEPTH,
WE'RE GOING TO HAVE THE DEPTH IN METERS,
WHICH IS EQUAL TO M,
IT'S GOING TO BE EQUAL TO -1,500 + 40
x A NUMBER OF MINUTES,
OR IN THIS CASE 40T.
NOW, IF WE WANT TO WRITE THIS EQUATION
IN SLOPE-INTERCEPT FORM, OR Y = MX + B FORM,
WE COULD REWRITE THIS AS M = 40T - 1,500.
THESE TWO EQUATIONS ARE EQUIVALENT,
BUT THIS FORM DOES MATCH THE FORM OF A LINEAR EQUATION
THAT WE HAVE BEEN STUDYING.
NOW, THE SECOND PART,
WE'RE GOING TO DETERMINE THE SUBMARINE'S POSITION
IN RELATION TO THE SURFACE AFTER 12 MINUTES.
WELL, 12 MINUTES WOULD BE THE VALUE OF T.
SO WHAT WE'LL DO IS USE THE EQUATION HERE
AND SUBSTITUTE 12 FOR T.
AND I'M GOING TO GO AHEAD AND USE THIS BLUE EQUATION HERE
BECAUSE THIS FORM OF THE EQUATION,
EVEN THOUGH IT'S NOT SLOPE-INTERCEPT FORM,
DOES SEEM A LITTLE BIT MORE INTUITIVE.
SO THE DEPTH IN METERS, AFTER 12 MINUTES,
IS GOING TO BE EQUAL TO -1,500 + 40 x 12,
AND THAT WOULD BE -1,500 + THIS SHOULD BE 480.
SO THIS IS GOING TO BE -1,020.
SO THE SUBMARINE IS 1,020 METERS BELOW THE SURFACE
AFTER 12 MINUTES.
WE DO WANT TO MAKE SURE THAT WHEN WE ANSWER THE QUESTION
WE INCLUDE THE UNITS.
AND BECAUSE IT'S NEGATIVE, THAT'S THE REASON WE KNOW
IT'S BELOW THE ACTUAL SURFACE OF THE WATER.
OKAY. HOPE YOU FOUND THIS HELPFUL.