Question

each month , a pond (2000 cubic meter of water) loses the same amount of water due to evaporation (128.25 cubic meter of water loses per months)

A.) represent the situation using a function in the form of an equation , representing the total amount of water in the pond after evaporation at certain number of months that have passed

B) what is the total amount of water in the pond (in m3) after it loses some by evaporation from February 1 to August 31

C.) evaluate the function at 1,2,3,4,5,6,7,8,9,10 months that have passed and express it numerically

D.) express through a graph in the Cartesian coodinate system ​

Answer 1

Step-by-step explanation:

A.) represent the situation using a function in the form of an equation , representing the total amount of water in the pond after evaporation at certain number of months that have passed

Answer 2

The correct answers are y = 2000 - 128.25x and 1102.25 $m^{3}$ respectively.

Given:

Loss of water per month = 128.25 cubic metres

The volume of the pond = 2000 cubic metre

To Find:

A.) Represent the situation in the form of an equation.

B) The total amount of water in the pond (in $m^{3}$) after it loses some by evaporation from February 1 to August 31

C.) The function at 1,2,3,4,5,6,7,8,9,10 months that have passed.

Solution:

We can simply solve this problem by using the following mathematical process.

A) Let y $m^{3}$ be the total amount of water in the pond and x $m^{3}$ be the number of months passed.

The equation will be

y = 2000 - 128.25x

B) Using the above equation, the total amount of water in the pond for 7 months i.e. February 1 to August 31 is

y = 2000 - (128.25)(7)

y = 1102.25 $m^{3}$

C) For the months 1 to 10 the values are as follows:

Month passed = 1

y = 2000 - (128.25)(1)

y = 1871.75 $m^{3}$

Months passed = 2

y = 2000 - (128.25)(2)

y = 1743.5 $m^{3}$

Months passed = 3

y = 2000 - (128.25)(3)

y = 1615.25 $m^{3}$

Months passed = 4

y = 2000 - (128.25)(4)

y = 1487 $m^{3}$

Months passed = 5

y = 2000 - (128.25)(5)

y = 1358.75 $m^{3}$

Months passed = 6

y = 2000 - (128.25)(6)

y = 1230.5 $m^{3}$

Months passed = 7

y = 2000 - (128.25)(7)

y = 1102.25 $m^{3}$

Months passed = 8

y = 2000 - (128.25)(8)

y = 974 $m^{3}$

Months passed = 9

y = 2000 - (128.25)(9)

y = 845.75 $m^{3}$

Months passed = 10

y = 2000 - (128.25)(10)

y = 717.5 $m^{3}$

Hence, the correct answers are y = 2000 - 128.25x and 1102.25 $m^{3}$ respectively.

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