Dead leaves accumulate on the ground in a forest at a rate of 3 grams per square centimeter per year. at the same time, these leaves decompose at a continuous rate of 75 percent per year.

a. write a differential equation for the total quantity, q, of dead leaves (per square centimeter) at time t.

b. sketch a solution to your differential equation showing that the quantity of dead leaves tends toward an equilibrium level. assume that initially (t=0) there are no leaves on the ground.

what is the initial quantity of leaves?

what is the equilibrium level?

does the equilibrium value attained depend on the initial condition?

a. yes
b. no

A - = 3 - 0.75D

B-  4 grams per square centimeter.

C-  Yes

Step-by-step explanation:

        = 3 - 0.75D

        if we put t = 0 in the equation we will get C = -4. This will give us an       equation:

          D = 4(1 - )

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: