document.write( "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.
\n" ); document.write( "1. Give the range of this function.
\n" ); document.write( "2. Make a table and graph this function.
\n" ); document.write( "3. Give the domain of this function. (show your calculations.) \n" ); document.write( "
Algebra.Com's Answer #492220 by mathgranny(13)\"\" \"About 
You can put this solution on YOUR website!
The equation is already given here , but if it wasn't how would you
\n" ); document.write( " arrive at the equation ?
\n" ); document.write( " Notice the rate of change : 80 meters per minute
\n" ); document.write( " The change is constant . 80 meters EVERY minute.
\n" ); document.write( " A constant rate of change indicates a linear equation which
\n" ); document.write( " can always be written as:
\n" ); document.write( " Output variable = rate of change(input variable) + starting value of output
\n" ); document.write( "How do you determine what the output and input variables are?
\n" ); document.write( " Look at the rate of change : 80 meters per minute .
\n" ); document.write( " There is one number and 2 words .
\n" ); document.write( " The FIRST word, meters, represents the OUTPUT variable .
\n" ); document.write( " Let's not use m, but ask what quantity is being measures in meters.
\n" ); document.write( " The DEPTH is being measured in meters, so we will use the variable
\n" ); document.write( " d to represent the output depth.
\n" ); document.write( " The SECOND word , minute, refers to the input variable
\n" ); document.write( " so use the variable m to represent the # of minutes.
\n" ); document.write( "The equation comes from this sentence:
\n" ); document.write( " To find depth of sub, multiply # of minutes times 80 and add it to the starting value -7500.
\n" ); document.write( " d = 80m + -7500
\n" ); document.write( " Table\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " m. d
\n" ); document.write( " # of min. depth, in meters
\n" ); document.write( " values of. values of
\n" ); document.write( " DOMAIN. RANGE
\n" ); document.write( " 0. -7500
\n" ); document.write( " 10. -6700
\n" ); document.write( " 50. -3500
\n" ); document.write( " 90. -300
\n" ); document.write( " .? 0. This is the highest value of sub, sea level , 0 elevation!!!
\n" ); document.write( " 100. 500. THIS cannot happen. The depth of the sub cannot be > 0!!!\r
\n" ); document.write( "\n" ); document.write( " The range has values from -7500 meters (starts 7500 BELOW sea level) to 0 meters.
\n" ); document.write( " The domain (possible values for input) starts at 0 minutes, but these # of minutes will
\n" ); document.write( " Stop when the sub has reached sea level when output or depth = 0.
\n" ); document.write( " How many minutes does it take for sub to surface , when d, depth = 0?
\n" ); document.write( " Go back to equation : d = 80 m + -7500
\n" ); document.write( " Replace d with 0
\n" ); document.write( " 0 = 80m + -7500
\n" ); document.write( " solve for m to get m = 93.75 minutes
\n" ); document.write( " So the domain, possible values for # of minutes in which the sub rises goes from
\n" ); document.write( " 0 to 93.75
\n" ); document.write( " When you graph this the y or vertical intercept, where graph crosses vertical axis,
\n" ); document.write( " has 0 for the x value, input value
\n" ); document.write( " so the point is (0, -7500). or. (0 min, -7500 meters)\r
\n" ); document.write( "\n" ); document.write( " The x or horizontal intercept , where graph crosses horizontal axis,
\n" ); document.write( " has 0 for the y or output value. (93.75. min, 0 meters )
\n" ); document.write( " Remember. y- intercept ? x = 0. (0,?)
\n" ); document.write( " x-intercept ? y = 0. ( ?, 0)
\n" ); document.write( " \n" ); document.write( "
\n" );