Ineed ! a diver made this table to show the relationship between time, x, and depth, y, for his last dive.

time (sec) 0 12 24 30 36
depth (ft) −18 −12 −6 −3 0
question 1
part a

what is the initial value for the function represented in the table?

−18

0.5

2

36
question 2
part b

what is the rate of change for the function represented in the table?

−18

0.5

2

36
question 3
part c

which statements about the situation are true?

select all that are correct.

it took the diver 18 seconds to reach the surface.

the diver ascended 12 foot per second.

the diver started 18 feet below the surface.

the diver descended 12 foot per second.

it took the diver 36 seconds to reach the surface.

Part A = -18

Part B = 0.5ft/sec

Part C =The diver started 18 feet below the surface and It took the diver 36 seconds to reach the surface.

Step-by-step explanation:

Here if we observe the Given function

Time(sec)   0   12   24   30   36

Depth(ft)   -18  -12   -6   -3    0

Part A

we can clearly observe from the table that at the initial value ie. at Time=0sec

the value of the function is nothing but the depth at the given time value which is -18 ft at time=0sec.

Part B

The rate of change of the given equation is

Take any two points in the given funtion like (0 , -18) and (30 , -3)

Now the rate of change is =

therefore the rate of change is 0.5 ft/sec

Part C

Clearly option C is correct which is the diver started at 18 feet below the surface . because At time =0 sec the diver's depth is -18ft Here the negative sign implies that the diver is below the surface of water.

Also it took 36 seconds to reach the surface because the diver's depth is zero at Time = 36 sec (from the graph).

The diver ascended at the rate of 0.5 ft/sec.