The water level in a retention pond started a 5 ft (60 in.) and decreased at a rate of 2 in./day during a 14-day drought. a tropical depression moved through at the beginning of the 15 day and proceed rain at an average rate of 2.4 in./day for 5 days.(a) write a piecewise - defined function to model the water level l(x) (in inches) as a function of the number of days x since the beginning of the drought.(b) graph the function.

Step-by-step explanation:

Since the water level is modelled for 2 different situations as

1) Period of Drought

Since the initial level of the pond at the start of our model is 60 inches and the rate of decrease is 2 inches per day the model can be replaced by a straight line

where

'y' is the water level in the pool at any time 't'

'C' is the water level at the start given as 60 inches

'm' is the rate of decrease of the water level given as -2 inches per day

't' is the time in days from the start of the model thus applying the given values we get

The water level at the end of the 14 days  is

Now since after 14 days the water level begins to rise at a rate 2.4 inches per day from a balance of 32 inches the water level is similarly modelled as above

Thus the combined function can be represented as

The graph is shown in the attached figure below

step-by-step explanation:

4  

25

5258y

54.

t5

5r

54

5856

542

5458

86

.8558.65

565

565

55898

786

8/95

5896

8656265

556478