Let p denote the population of the United States (in millions) in the year t, and assume that p is defined implicitly as a function of t by the equation
0 = ln p + 45.8177 − ln (2225 − 4.2381p) − 0.02225t.
Use implicit differentiation to show that the rate of change of p with respect
to t satisfies the equation:
dp
dt = 10−5p(2225 − 4.238p).

dp/dt = 10⁻⁵p(2225 − 4.2381p)

Step-by-step explanation:

Since the function is

0 = ln p + 45.8177 − ln (2225 − 4.2381p) − 0.02225t

Differentiating the function implicitly with respect to time, we have

d0/dt = d[ln p + 45.8177 − ln (2225 − 4.2381p) − 0.02225t]/dt

d0/dt = d[ln p]/dt + d[45.8177]/dt − d[ln (2225 − 4.2381p)]/dt − d[0.02225t]/dt

0 = (1/p)dp/dt + 0 − (1/(2225 − 4.2381p)) × -4.2381 dp/dt − 0.02225

0 = (1/p)dp/dt + 4.2381 dp/dt/(2225 − 4.2381p)  − 0.02225

-(1/p)dp/dt - 4.2381 dp/dt/(2225 − 4.2381p)  = − 0.02225

(1/p)dp/dt + 4.2381 dp/dt/(2225 − 4.2381p)  =  0.02225

Factorizing out dp/dt from the left hand side, we have

[(1/p) + 4.2381/(2225 − 4.2381p)]dp/dt  =  0.02225

taking L.C.M of the left-hand-side and simplifying, we have

[((2225 − 4.2381p + 4.2381p)/p(2225 − 4.2381p)]dp/dt  =  0.02225

[2225/p(2225 − 4.2381p)]dp/dt  =  0.02225

dividing both sides by2225, we have

[1/p(2225 − 4.2381p)]dp/dt  =  0.02225/2225

[1/p(2225 − 4.2381p)]dp/dt  =  0.00001

[1/p(2225 − 4.2381p)]dp/dt  = 10⁻⁵

multiplying both sides by p(2225 − 4.2381p), we have

p(2225 − 4.2381p)[1/p(2225 − 4.2381p)]dp/dt  = 10⁻⁵p(2225 − 4.2381p)

So, dp/dt = 10⁻⁵p(2225 − 4.2381p)

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )

the total estimated nappy use.=10,500,000

step-by-step explanation:

given that on an average the average baby uses 3528 napkins.

in a particular year 2014, the number of births were 299697 in new south wales.

rounding off the number of births to the nearest hundred thousand we have

no of birtsh = 300000

also rounding off the average usage to nearst thousand we get

average use of a baby = 3500

hence total number of nappy estimated to be used = 3500x300000

= 10,500,000

answer is 10,500,000 nappies