SOLUTION: A submarine that is 7500 meters below sea level surfaces at a rate of 80 meters per minute. The depth of the submarine after m minutes is given by d(m)=-7500+80m. 1. Give the rang

Question 817813: A submarine that is 7500 meters below sea level surfaces at a rate of 80 meters per minute. The depth of the submarine after m minutes is given by d(m)=-7500+80m.
1. Give the range of this function.
2. Make a table and graph this function.
3. Give the domain of this function. (show your calculations.)
Answer by mathgranny(13) (Show Source): You can put this solution on YOUR website!
The equation is already given here , but if it wasn't how would you
arrive at the equation ?
Notice the rate of change : 80 meters per minute
The change is constant . 80 meters EVERY minute.
A constant rate of change indicates a linear equation which
can always be written as:
Output variable = rate of change(input variable) + starting value of output
How do you determine what the output and input variables are?
Look at the rate of change : 80 meters per minute .
There is one number and 2 words .
The FIRST word, meters, represents the OUTPUT variable .
Let's not use m, but ask what quantity is being measures in meters.
The DEPTH is being measured in meters, so we will use the variable
d to represent the output depth.
The SECOND word , minute, refers to the input variable
so use the variable m to represent the # of minutes.
The equation comes from this sentence:
To find depth of sub, multiply # of minutes times 80 and add it to the starting value -7500.
d = 80m + -7500
Table

m. d
# of min. depth, in meters
values of. values of
DOMAIN. RANGE
0. -7500
10. -6700
50. -3500
90. -300
.? 0. This is the highest value of sub, sea level , 0 elevation!!!
100. 500. THIS cannot happen. The depth of the sub cannot be > 0!!!
The range has values from -7500 meters (starts 7500 BELOW sea level) to 0 meters.
The domain (possible values for input) starts at 0 minutes, but these # of minutes will
Stop when the sub has reached sea level when output or depth = 0.
How many minutes does it take for sub to surface , when d, depth = 0?
Go back to equation : d = 80 m + -7500
Replace d with 0
0 = 80m + -7500
solve for m to get m = 93.75 minutes
So the domain, possible values for # of minutes in which the sub rises goes from
0 to 93.75
When you graph this the y or vertical intercept, where graph crosses vertical axis,
has 0 for the x value, input value
so the point is (0, -7500). or. (0 min, -7500 meters)
The x or horizontal intercept , where graph crosses horizontal axis,
has 0 for the y or output value. (93.75. min, 0 meters )
Remember. y- intercept ? x = 0. (0,?)
x-intercept ? y = 0. ( ?, 0)

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